Neela Nataraj, Professor, Department of Mathematics, IIT Bombay

Career

  • Lecturer at Institute of Technology and Management, Gurgaon (August 1998 - June 1999)
  • Senior Lecturer at Indraprastha University, Delhi (June 1999 - December 1999)
  • Senior Lecturer at Indian Institute of Technology Delhi (December 1999 - April 2002)
  • Assistant Professor at Indian Institute of Technology Delhi (April 2002 - June 2003)
  • Assistant Professor at Indian Institute of Technology Bombay (June 2003 - February 2009)
  • Associate Professor at Indian Institute of Technology Bombay (February 2009 - August 2014)
  • Professor at Indian Institute of Technology Bombay (September 2014 - till date)

Administrative Positions

Institute:

  • Dean (Strategy), IIT Bombay, November 2025 onwards
  • Dean (Faculty Affairs), IIT Bombay, May 2021- May 2025
  • Professor-in-Charge, IIT Bombay-Monash Research Academy, April 2019-April 2021
  • Head, Department of Mathematics, IIT Bombay, Dec. 2015 - Dec. 2018
  • Convener, Women’s Cell and Internal Complaints Committee, IIT Bombay, 2015 - 2017
  • Vice Chairperson, Joint Admission Test for M.Sc. (JAM), IIT Bombay, Oct. 2009 - Sept. 2010

National:

  • Secretary, Mumbai Chapter, NASI, 2025 onwards
  • Member, Apex Committee, National Center for Mathematics (NCM), 2020 onwards
  • Member, International Advisory Committee, Indian Women and Mathematics (IWM), 2023 onwards
  • Chair, Executive Committee, Indian Women and Mathematics (IWM), April 2019- March 2022
  • Executive Committee Member, Indian Women and Mathematics (IWM), 2016- March 2022

International:

  • Member of the panel for Southeastern Asia & Pacific, The Chebyshev grant, International Congress of Mathematicians (ICM) 2022
  • Member, Organizing Committee of World Meeting for Women in Mathematics (WM)2 (a satellite conference of ICM 2022)
  • Member (Responsible for Grant management), IMU CWM, January 2019 - 2022
  • Member, Core Committee of BRICS Mathematics Conferences, since 2017
  • Associate Member, International Mathematics Union Committee for Women in Mathematics (IMU CWM), 2015 - 2018

Specialization

Numerical Analysis & Scientific Computing, Finite Element Methods and Applied Mathematics

Education

Received Ph. D. from Department of Mathematics, IIT Delhi in 1998 on Mixed Finite Element Analysis of Fourth Order Elliptic Source/Eigenvalue Problems in Convex Domains after graduating with Masters from Department of Mathematics, University College, Thiruvananthapuram, Kerala (1990).

Editorial board Memberships

  • Associate Editor, SIAM Journal on Scientific Computing, 2026 onwards
  • Member, Editorial Board, Indian Journal of Pure and Applied Mathematics, 2025 onwards
  • Member, Editorial Board, ESAIM: Mathematical Modelling and Numerical Analysis, March 2021 onwards
  • Associate Editor, Numerical Analysis and Scientific Computing: Advances in Discrete and Continuous Models, June 2021 onwards
  • Member, Editorial Board, Computational Methods in Applied Mathematics,2019-2025
  • Member, Editorial Board, Computers & Mathematics with Applications, 2015-2024
  • Member, Editorial Board, Proceedings-Mathematical Sciences, Indian Academy of Sciences, 2015-2021
  • Associate Editor, International Journal of Numerical Analysis and Modelling, Series B, 2010-2014
  • Guest Editor, Special Issue on Recent Advances in PDE: Theory, Computations and Applications, Computational Methods in Applied Mathematics (2019)

Awards & Honours

  • Recipient of JC Bose Grant, Anusandhan National Research Foundation (ANRF), 2025-2030
  • DAAD Research Ambassador, 2025-2028
  • Fellow of the Indian National Science Academy (INSA), 2025 onwards
  • Featured in Women of Mathematics from around the world. A gallery of portraits produced by the Women in Math Project: https://womeninmath.net/project/about-the-project/, 2023
  • SERB POWER Fellowship, Science & Engineering Research Board, Department of Science and Technology (2021)
  • Institute Chair Professor, Indian Institute of Technology Bombay, 2021-2024
  • Fellow of the Indian Academy of Sciences (IAS) (2021)
  • The 34th P.L. Bhanagar Memorial Award Lecture in the 86th Annual Conference of Indian Mathematical Society (2020)
  • Fellow of the National Academy of Sciences (NASI) (2019)
  • Indian National Science Academy (INSA) Teachers Award (2019)
  • Featured in the film Journeys of Women in Mathematics created by the International Mathematical Union Committee for Women in Mathematics, filmed and edited by Micro-Documentaries and funded by Simons Foundation (https://www.youtube.com/watch?v=uNJ7riiPHOY)
  • S. P. Sukhatme Excellence in Teaching Award (2016)
  • Simons Visiting Professorship, MFO, Oberwolfach, October 2015
  • IIT Bombay Excellence in Teaching Award (2012)
  • IIT Bombay Excellence in Teaching Award (2008)
  • DAAD Research Grant (May 18- June 20, 2006) for Research visit to Humboldt University, Berlin
  • Appreciation letter from Director, IIT Delhi (2002) for good performance in the five elements:
    teaching, academic research, sponsored research, academic management and honours/awards. (Rating : above 4 out of 5)
  • National Board of Higher Mathematics Research Award , Department of Atomic Energy (1990)
  • Council of Scientific and Industrial Research Research Award (1990)
  • First rank in M.Sc (Kerala University) (1990)
  • Kerala University Merit Scholarship during Graduation (1986-88) and Post-Graduation (1988-90)

Publications

  1. Neela Nataraj, Ramesh Sau, Variational based NN and PINN for the Poisson problem. Indian Journal of Pure and Applied Mathematics 57:143–174 (2026)
  2. Carsten Carstensen, Asha K. Dond, Ruma R. Maity, Neela Nataraj, and Lara Theallier, Adaptive Crouzeix--Raviart finite elements for a non-convex Ginzburg--Landau model for nematic liquid crystalsComputer Methods in Applied Mechanics and Engineering 452(A), Article 118646 (2026)
  3. Neela Nataraj, Ricardo Ruiz-Baier, and Aamir Yousuf, Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem. Accepted for publication in Comput. Methods Appl. Math. (2025) https://doi.org/10.1515/cmam-2025-0002
  4. Avijit Das, Neela Nataraj, and Gopikrishnan C Remesan, Semi and fully-discrete analysis of extended Fisher-Kolmogorov equation with nonstandard FEMS for space discretisation. Accepted for publication in Journal of Scientific Computing (2025)
  5. Shantiram Mahata, Neela Nataraj, and Jean-Pierre Raymond, Lowest-order nonstandard finite element methods for time-fractional biharmonic problem. ESAIM Math. Model. and Numer. Anal. 59:43-71 (2025)
  6. Carsten Carstensen, Benedikt Grassle and Neela Nataraj, A posteriori error control for fourth-order semilinear problems with quadratic nonlinearity. SIAM J. Numer. Anal. 62(2): 919-945 (2024)
  7. Carsten Carstensen, Benedikt Grassle and Neela Nataraj, Unifying a posteriori error analysis of five quadratic discretisations for the biharmonic equation. J. Numer. Math. 2024; 32(1): 77–109 (2024)
  8. Wasim Akram, Debanjana Mitra, Neela Nataraj and Mythily Ramaswamy, Feedback stabilization of a parabolic coupled system and its numerical study. Mathematical Control and Related Fields (MCRF) 14(2): 695-746 (2024)
  9. Asha K. Dond, Neela Nataraj and Subham Nayak, Convergence of adaptive Crouzeix-Raviart and Morley FEM for distributed optimal control problems. Comput. Methods Appl. Math. (2024)
  10. Avijit Das, Bishnu Lamichhanne and Neela Nataraj, A unified mixed finite element method for fourth-order time-dependent problems using biorthogonal systems. Computers and Mathematics with Applications (CAMWA) 165, 52-69 (2024)
  11. Rekha Khot, Neela Nataraj and Nitesh Verma, Conforming VEM for general second-order elliptic problems with rough data on polygonal meshes and its application to a Poisson inverse source problem. Mathematical Models and Methods in Applied Sciences (M3AS) 33(14), 2963-3007 (2023)
  12. Ruma R. Maity, Apala Majumdar and Neela Nataraj, A priori and a posteriori error analysis for semilinear problems in liquid crystals. ESAIM Math. Model. and Numer. Anal. (2023)
  13. Carsten Carstensen, Neela Nataraj, Gopikrishnan C. Remesan, and Devika Shylaja, Unified a priori analysis of four second-order FEM for fourth-order quadratic semilinear problems. Numerische Mathematik (2023)
  14. Bishnu Lamichhanne, Neela Nataraj and Deepanshu Verma, A Mixed Finite Element Method using a biorthogonal System for optimal control problems governed by a biharmonic equation. Proceedings of the 20th Biennial Computational Techniques and Applications Conference, CTAC-2022 (64), C45--C61, ANZIAM J. (2022)
  15. Sudipto Chowdhury, Asha Dond, Neela Nataraj and Devika Shylaja, A posteriori error analysis for a distributed optimal control problem governed by the von Kármán equations. ESAIM Math. Model. and Numer. Anal. 56(5), 1655-1686(2022)
  16. Jérôme Droniou, Neela Nataraj and Gopikrishnan Chirappurathu Remesan, Convergence analysis of a numerical scheme for a tumour growth model. IMA J. Numer. Anal., 42(2), 1180-1230 (2022) https://doi.org/10.1093/imanum/drab016, http://arxiv.org/abs/1910.07768
  17. Carsten Carstensen and Neela Nataraj, Lowest-order equivalent nonstandard finite element methods for biharmonic plates. ESAIM Math. Model. and Numer. Anal. 56, 41–78 (2022) http://arxiv.org/abs/2102.08125
  18. Carsten Carstensen, Neela Nataraj and Amiya K. Pani, Stability of mixed FEMs for non-selfadjoint indefinite second-order linear elliptic PDEs. Numerische Mathematik, 150, 975-992 (2022)
  19. Ruma Rani Maity, Apala Majumdar, Neela Nataraj, Parameter dependent finite element analysis for ferronematics solutions. Computers and Mathematics with Applications (CAMWA)103, 127-155 (2021)
  20. Carsten Carstensen, S. Gaddam, Neela Nataraj, A. K. Pani and D. Shylaja, Morley finite element method for the von Kármán obstacle problem. ESAIM Math. Model. and Numer. Anal. 55, 1873–1894 (2021)https://arxiv.org/abs/2009.03205
  21. Carsten Carstensen and Neela Nataraj, A priori and a posteriori error analysis of the Crouzeix-Raviart and Morley FEM with original and modified right-hand sides. Comput. Methods Appl. Math. 21(2), 289-315 (2021) http://arxiv.org/abs/2102.08117 (2021) http://arxiv.org/abs/2102.08117
  22. Carsten Carstensen, Gouranga Mallik and Neela Nataraj, Nonconforming finite element discretization for semilinear problems with trilinear nonlinearity. IMA J. Numer. Anal. 41, 164-205 (2021) https://doi.org/10.1093/imanum/drz071
  23. Jerome Droniou, Neela Nataraj and Devika Shylaja, Hessian discretisation method for fourth order semilinear elliptic equations Comput. Math. (2020) http://arxiv.org/abs/2004.09842
  24. Ruma Rani Maity, Apala Majumdar and Neela Nataraj, A priori and a posteriori error analysis for the Nitsche’s method applied to a reduced Landau-de Gennes problem. Comput. Methods Appl. Math (2020).
  25. Carsten Carstensen and Neela Nataraj, Adaptive Morley FEM for the von K´arm´an equations with optimal convergence rates. SIAM J. Numer. Anal. (2020) http://arxiv.org/abs/1908.08013
  26. Sudipto Chowdhury, Neela Nataraj and Devika Shylaja, Morley FEM for a distributed optimal control problem governed by the von K´arm´an equations Accepted for publication in Comput. Methods Appl. Math. https://doi.org/10.1515/cmam-2020-0030. (30 pages) (2020)
  27. Ruma Rani Maity, Apala Majumdar and Neela Nataraj, Discontinuous Galerkin finite element methods for the Landau-de Gennes Minimization problem of liquid crystals, https://arxiv.org/abs/1907.06847 Accepted for publication in IMA J. Numer. Anal. (34 pages) (2020)
  28. Neela Nataraj and A.S. Vasudeva Murthy, Finite element methods: Research in India over the last decade. Indian Journal of Pure and Applied Mathematics 50 no. 3, 739–765 (2019)
  29. Carsten Carstensen, Gouranga Mallik and Neela Nataraj, A priori and a posteriori error control of discontinuous Galerkin finite element method for von Karman equations. IMA J. of Numer. Anal. 39 (1), 167-200 (2019).
  30. Carsten Carstensen, Asha K. Dond, Neela Nataraj and Amiya K. Pani, Three first-order finite volume element methods for Stokes equations compete under minimal regularity assumptions. SIAM J. Numer. Anal. 56(4), pp. 2648-2671 (2018).
  31. Gouranga Mallik, Neela Nataraj and Jean-Pierre Raymond, Error estimates for the numerical approximation of a distributed optimal control problem governed by the von Karman equations. ESAIM: M2AN (Math. Model. and Numer. Anal.) 52, pp. 1137-1172 (2018).
  32. Jerome Droniou, Neela Nataraj and Devika S, Numerical analysis for the pure Neumann control problem using the gradient discretization method. Comput. Meth. Appl. Math. 18(4), 609-637 (2018).
  33. Jerome Droniou and Neela Nataraj, Improved L2 estimate for gradient schemes and super-convergence of HMM and TPFA methods. IMA J. Numer. Anal. 38(3), pp.1254-1293 doi: 10.1093/imanum/drx028. url:https://arxiv.org/abs/1602.07359. (2018).
  34. Jerome Droniou, Neela Nataraj and Devika S, The gradient discretization method for optimal control problems, with super-convergence for non-conforming finite elements and mixed-hybrid mimetic finite differences.SIAM J. Control Optim. 55 (6), pp. 3640-3672, (2017).
  35. Asha K. Dond, Neela Nataraj and Amiya K. Pani, Convergence analysis of adaptive finite element methods for non-self adjoint and indefinite elliptic problems. IMA J. Numer. Anal. 37 (2): 832-860 (2017).
  36. Asha K. Dond, Thirupathi Gudi and Neela Nataraj, On a nonconforming finite element approximation for optimal control of the obstacle problem. Comput. Meth. Appl. Math.,16(4): 653-666 (2016).
  37. Gouranga Mallik and Neela Nataraj, Conforming finite element methods for the von K´arm´an equations. Adv. Comput. Math. 42 (5): 1031-1054 (2016).
  38. Carsten Carstensen, Neela Nataraj and Amiya K. Pani, Unified Analysis and Comparison Results for First Order FVM. IMA J. Numer. Anal. 36 (3): 1120-1142. (2016).
  39. Gouranga Mallik and Neela Nataraj, Nonconforming finite element methods for the von K´arm´an equations. M2AN Math. Model. and Numer. Anal.50 (2): 433-454 (2016).
  40. Carsten Carstensen, Asha K. Dond, Neela Nataraj and Amiya K. Pani, A posteriori mixed finite element error analysis for non-self adjoint and indefinite elliptic problems. Numer. Math. 133(3): 557-597 (2016) (2016).
  41. Gouranga Mallik and Neela Nataraj, Conforming and nonconforming finite element methods for the canonical von K´arm´an equations. International Journal of Advances in Engineering Sciences and Applied Mathematics, DOI 10.1007/s12572-015-0137-y (2015).
  42. Carsten Carstensen, Dietmar Gallistl and Neela Nataraj, Comparison Results of non standard P2 Finite Element Methods for the Biharmonic Problem. ESAIM: M2AN (Math. Model. and Numer.Anal.) 49 pp. 977-990 (2014).
  43. Thirupathi Gudi, Neela Nataraj and Kamana Porwal, An interior penalty method for distributed optimal control problems governed by the biharmonic operator. Computers and Mathematics with Applications 68 ( 12 ) pp. 2205 - 2221 (2014)(2014).
  44. Saumya Bajpai and Neela Nataraj, On a two-grid Crank-Nicolson method combined with a finite element scheme for the equations of motion arising in Kelvin-Voigt model. Computers and Mathematics with Applications 68 ( 12 ) pp. 2277 - 2291 (2014).
  45. Nupur Gupta and Neela Nataraj, A Dual Weighted Residual Method for an Optimal Control Problem of Laser Surface Hardening of Steel. Mathematics and Computers in Simulation 103, pp. 12-32 (2014).
  46. Saumya Bajpai, Neela Nataraj and Amiya K. Pani, On a two-grid finite element scheme for the equations of motion arising in Kelvin-Voigt model. Adv. Comput. Math. 40, pp. 1043-1071 (2014).
  47. Nupur Gupta and Neela Nataraj, A posteriori error estimates for an optimal control problem of laser surface hardening of steel. Adv. Comput. Math. 39(1), pp. 69-99 (2013).
  48. T. Gnana Bhaskar, S. Hariharan and Neela Nataraj, Heatlet approach to diffusion equation on a semi-infinite region. Neural, parallel & scientific computations, 21 (3-4), pp. 375-391 (2013).
  49. Sangita Yadav, Amiya K. Pani, and Neela Nataraj, Superconvergent discontinuous Galerkin methods for linear non-selfadjoint and indefinite elliptic problems. J. Sci. Comput. 54(1), pp. 45-76 (2013).
  50. Thirupathi Gudi, Hari Shanker Gupta, and Neela Nataraj, Analysis of an interior penalty method for fourth order problems on polygonal domains. J. Sci. Comput. 54(1), pp. 177-199 (2013).
  51. Saumya Bajpai, Neela Nataraj, Amiya K. Pani, Pedro Damazio and Jin Yun Yuan, Semidiscrete Galerkin method for equations of motion arising in Kelvin-Voigt model of viscoelastic fluid flow. Numer. Methods for Partial Differential Equations 29(3), pp. 857-883 (2013).
  52. Saumya Bajpai, Neela Nataraj and Amiya, K. Pani, On fully discrete finite element schemes for equations of motion of Kelvin-Voigt fluids. Int. J. Numer. Anal. Model. 10 (2), pp. 481-507 (2013).
  53. Sajid Memon, Neela Nataraj and Amiya K.Pani, An a posteriori error analysis of mixed finite element Galerkin approximations to second order linear parabolic problems. SIAM J. Numer. Anal. 50(3), pp. 1367-1393 (2012).
  54. Nupur Gupta and Neela Nataraj, An hp discontinuous Galerkin method for the optimal control problem of laser surface hardening of steel. ESAIM Math. Model. Numer. Anal. (M 2 AN) 45(6), pp. 1081-1113 (2011).
  55. Shalini Baskar, Neela Nataraj and P.K. Bhattacharyya, A parallel mixed-hybid finite element method for anisotropic plate bending problems. Advances in Engineering Software 43(1), pp. 87-95 (2011).
  56. Debasish Pradhan, Shalini Baskar, Neela Nataraj and Amiya K. Pani, A Robin type non-overlapping domain decomposition procedure for second order elliptic problems. Adv. Comput. Math. 34(4), pp. 339-368 (2011).
  57. Nupur Gupta, Neela Nataraj and Amiya K. Pani, On the optimal control problem of laser surface hardening. Int. J. Numer. Anal. Model. 7(4), pp. 667-680 (2010).
  58. Sarvesh Kumar, Neela Nataraj and Amiya K. Pani, Discontinuous Galerkin finite volume element methods for second order elliptic problems. Numer. Methods for Partial Differential Equations 25(6), pp. 1402-1424 (2009).
  59. Neela Nataraj, A mixed finite element method for fourth order eigenvalue problems. Appl. Math. Comput. 213 (1), pp. 60-72 (2009).
  60. Thirupathi Gudi, Neela Nataraj and Amiya K. Pani, On L 2 error estimate for non-symmetric interior penalty Galerkin approximation to linear elliptic problems with nonhomogeneous Dirichlet data. J. Comput. Appl. Math., 228 (1) pp. 30-40 (2009).
  61. Ajit Patel, Amiya K. Pani and Neela Nataraj, Mortar element methods for parabolic problems. Numer. Methods for Partial Differential Equations, 24(6) pp. 1460-1484 (2008).
  62. Thirupathi Gudi, Neela Nataraj and Amiya K. Pani, Mixed discontinuous Galerkin method for the biharmonic equation. J. Sci. Comput., 37 (2), pp. 139-161, (2008).
  63. Thirupathi Gudi, Neela Nataraj and Amiya K. Pani, An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of non-monotone type. Math. Comp., 77, pp.731-756 (2008).
  64. Debasish Pradhan, Neela Nataraj, Amiya K. Pani, An explicit/implicit Galerkin domain decomposition procedure for parabolic integro-differential equations. J. Appl. Math. Comput., 28 (1-2), pp.295-311 (2008).
  65. Pritam S.Mantri, Neela Nataraj and Amiya K. Pani, A qualocation method for Burgers' equation. J. Comput. Appl. Math., 213(1), pp. 1-13 (2008).
  66. Sarvesh Kumar, Neela Nataraj, Amiya K. Pani, The finite volume element method for second order hyperbolic equation. International Journal of Numerical Analysis and Modeling, 5, pp. 132-151 (2008).
  67. Thirupathi Gudi, Neela Nataraj and Amiya K. Pani, hp-discontinuous Galerkin Methods for strongly non-linear elliptic boundary value problems. Numer. Math., 109(2), pp. 233-268 (2008).
  68. T. Gnana Bhaskar, S. Hariharan and Neela Nataraj, Heatlet approach to diffusion equation on unbounded domains. Appl. Math. Comput., 197 (2), pp. 891-903 (2008).
  69. Ambit K. Pany, Neela Nataraj and Sangita Singh, A new mixed finite element method for Burgers' equation. J. Appl. Math. Comput. 23, pp. 43-55 (2007).
  70. Kshitij Kulsreshtha and Neela Nataraj, A parallel mixed finite element implementation for approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems.(Short Communication) Journal of Sound and Vibration, 285, pp. 1242-1254 (2005).
  71. Kshitij Kulsreshtha, Neela Nataraj and Michael Jung, A parallel mixed finite element implementation of fourth order plate bending problems in distributed memory environments. Appl. Math. Comput., 163, pp. 253-274 (2005).
  72. Kshitij Kulsreshtha, Neela Nataraj and Michael Jung, Performance of a parallel mixed finite element implemenatation for fourth order clamped anisotropic plate bending problems in distributed memory environments. Appl. Math. Comput., 155, pp. 753-777 (2004).
  73. P. K. Bhattacharyya and Neela Nataraj, Error Estimates for isoparametric mixed finite element solution of fourth order elliptic problems with variable coefficients. Comput. Mech., 28(6), pp.435-455 (2002).
  74. P. K. Bhattacharyya and Neela Nataraj, Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems with variable coefficients. M2AN Math. Model. and Numer. Anal. , 36(1), pp. 1-32 (2002).
  75. P. K. Bhattacharyya and Neela Nataraj, On combined effect of boundary approximation and numerical integration on mixed finite element solution of fourth order elliptic problems with variable coefficients. M2AN Math. Model. and Numer. Anal., 33(4), pp. 807-836 (1999).
  76. Neela Nataraj, P. K. Bhattacharyya, S. Balasundaram and S. Gopalsamy, On a mixed hybrid finite element method for anisotropic plate bending problems. Internat. J. Numer. Methods Engrg., 39(23), pp. 4063-4089 (1996).

Conference & Other Publications

  1. Jennifer A Flegg and Neela Nataraj, Mathematical Modelling and Avascular Tumour Growth-Interdisciplinary Research Resonance - Journal of Science Education 24(3) pp. 313-325 (2019).
  2. Neela Nataraj, Presentation of the Special Issue on Recent Advances in PDE: Theory, Computations and Applications, https://doi.org/10.1515/cmam-2019-0027(2019).
  3. Thirupathi Gudi, Neela Nataraj and Kamana Porwal, A C0 interior penalty method for an optimal control problem governed by the biharmonic operator, Proceedings of the Indo-German Workshop on Advances in PDE Modeling and Computation, October 21-25, 2013.
  4. Sarvesh Kumar, Neela Nataraj and Amiya K. Pani, Finite volume element method for the incompressible miscible displacement problems in porous media, PAMM. Proc. Appl. Math. Mech. 7, 2020015-2020016 (2007) /DOI 10.1002/pamm.200700090.
  5. Neela Nataraj and Ambit Kumar Pany, An H 1 -Galerkin mixed finite element method for linear and nonlinear parabolic problems, Proceedings of the Conference on Differential and Difference Equations and Application, Hindavi Publishing Corporation, 851-860 (2006).
  6. Neela Nataraj, A mixed finite element method for fourth order eigenvalue problems, Proc. Appl. Math. Mech. (PAMM) 4, 358-359 (2004).
  7. Kshitij Kulsreshtha, Neela Nataraj and Michael Jung, Performance of a mixed finite element implemenatation for fourth order clamped anisotropic plate bending problems in SIMDdistributed memory environments, Proceedings of ICIWIM 2002, IIT Bombay.

Research Report

  • P. K. Bhattacharyya, Neela Nataraj. Isoparametric mixed finite element approximation of eigenvalues and eigenvectors of fourth order eigenvalue problems with variable coefficients, Research Report No. R 98021, Laboratory of Pierre and Marie Curie University of Paris, Paris (1998).
  • Neela Nataraj (joint with Gouranga Mallik). Finite element methods for the von Karman equations, Oberwolfach Research Report No. 43/2015 (2015).
  • Neela Nataraj (joint with Carsten Carstensen and Gouranga Mallik). A priori control of DGFEM for the von Karman equations, Oberwolfach Research Report No. 48/2018.

Students

I had the privilege of teaching a great many students in my career who made teaching a wonderful learning experience for me. It would be impossible to name all of them, but here is a shorter list of students I have worked more closely with.

Currently supervising following students' doctoral research

  • Shivani Mangal on Smectic liquid crystals
  • Siyad Rahman on Time-dependent plate bending problems with Professor Ricardo Ruiz Baier (Joint supervisor, Monash University)
  • Aamir Yousuf on Interface conditions for elasticity diffusion with Professor Ricardo Ruiz Baier (Joint supervisor, Monash University)

Also supervised following students' doctoral research

Supervised following students' Masters research:

  • Shreyas Kirwai on Mathematical modeling of hot forging die wear (2011, co-supervised by Professor Amiya K. Pani and Mukund Mavalankar)
  • Bibekanda Maji on Discontinuous Galerkin Methods (2010)
  • Debabrata Das on Multigrid Methods (2008)
  • Priyanka Sadhani on Finite Element Methods for solving integro-differential equations (2007)
  • Deepak Sharma on Finite Volume Methods for PDEs (2005)
  • Kshitij Kulshreshtha on A parallel mixed finite element implementation for approximation of fourth order elliptic source problem using DD approach and approximation of eigenvalues of fourth order elliptic eigenvalue problems using the Lanczos method (2003)
  • Yogesh Joshi on Implementation of Lanczos method for solving eigenvalue problems (2003, co-supervised by Niladri Chatterjee [IITD])
  • Aditya Kumar on Computer Implementation of Argyris element (2001)

Mentored post-doctoral research for Dr. Divya Venkatraman during April 2014-October 2014 and Dr. Shalini Baskar between April 2007 and April 2009. Currently mentoring Sudipto Chowdhury in his post-doctoral research.

Projects

I have undertaken the following sponsored research projects:

  • Numerical analysis of liquid crystals sponsored by DST-DAAD PPP - 15 lakhs for 2 years from 2023
  • Finite element methods for phase field crystal equation sponsored by SERB POWER - 38 lakhs for 3 years from 2021
  • Mathematics and Computation of Plates (PIs Carsten Carstensen and Neela Nataraj) SPARC, MHRD - 49 lakhs for 2 years from 2019
  • Finite element methods for nonlinear plate bending problems and optimal control problems governed by nonlinear plates- 6.6 lakhs for 3 years from 2018
  • Finite Element Methods for Parameter Identification Problems in Elliptic Partial Differential Equations - M. T. Nair, A. K. Pani as Co-PIs
  • National Programme on Differential Equations: Theory, Computation & Applications (Co-PI) sponsored by Department of Science and Technology, India with approximately 5 crores grant for 5 years from 2012
  • Theoretical and Computational Studies of Kelvin - Voigt model of viscoelastic fluids (Co-PI) sponsored by Department of Science and Technology, Indo-Brazil Project with approximately 9 lacs grant for 3 years from 2009
  • The Oldroyd model of viscoelastic fluids- Theoretical and Computational Studies (Co-PI) sponsored by Department of Science and Technology, India with approximately 20 lacs grant for 3 years from 2008
  • A parallel mixed finite element implementation of IV order elliptic source/eigenvalue problems in distributed memory environments sponsored by IRCC, IIT Bombay with 3 lacs grant in 2003
  • Parallelization of mixed finite element methods for source/eigenvalue problems sponsored by Department of Science and Technology, India with 4 lacs grant for 3 years from 2001
  • Computer implementation procedures for mixed finite element methods for fourth order elliptic source/eigenvalue problems sponsored by IRD, IIT Delhi with 0.74 lacs grant for 18 months from 2000

Short Courses

  1. Discrete De Rham Method by Prof. Jerome Droniou, University of Montpellier (Supported by ANRF JCB Grant)

    2. I will start by explaining what the de Rham complex is and, through examples, why it is important for the theoretical analysis of certain partial differential equations involving gradient, curl or divergence operators. I will then present the Discrete De Rham (DDR) method, an arbitrary-order discretisation of the de Rham complex that is applicable on generic polyhedral meshes. We will see that the construction of the method is entirely based on mimicking integration-by-parts properties (for the gradient, the curl and the divergence), and is hierarchical: we construct the space and discrete operators starting from the edges, then going on the faces, then on the elements. I will highlight the main properties of the DDR method, which allows for convergence analysis of schemes built on it. A particular focus will be on the notion of "adjoint consistency" which arises due to the non-conformity of the method. I will detail such a convergence analysis on the example of the Stokes equations in curl-curl formulation.

  2. The Mathematics of Liquid Crystals by Prof. Apala Majumdar, University of Manchester (Supported by ANRF JCB Grant)

    3. This mini-course will comprise four lectures on the mathematics of liquid crystals and modelling of liquid crystal applications. Liquid crystals are complex materials that combine fluidity with the ordering of solids and consequently, have fascinating physical, mechanical and rheological properties. Liquid crystals are best known as the working material of choice for the multi-billion dollar display industry. We will give a non-technical introduction to liquid crystals - their history, physics and applications, followed by an overview of the main mathematical theories for liquid crystals. We will conclude the lecture course with examples of mathematical modelling of real-life liquid crystal systems.

CIMPA

CIMPA Notes

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