Published Papers in Journals:

  1. Deepjyoti Goswami, A. K. Pani and Sangita Yadav (Accepted), Optimal L2 estimates for semidiscrete Galerkin methods for parabolic integro-differential equations with nonsmooth data, Australian and New Zealand Industrial and Applied Mathematics Journal (2013).

  2. S. Bajpai, N. Nataraj and A. K. Pani (Accepted), On a two-grid finite element scheme for the equations of motion arising in the Kelvin-Voigt model , Adv. Comp. Math. (2013).

  3. Amiya K. Pani, Ambit K.Pani, P. Damazio and J. Y. Yuan (Accepted),A modified nonlin- ear spectral Galerkin method for the equations of motion arising in the Kelvin-Voigt fluids, Applicable Analysis, 2013.

  4. Deepjyoti Goswami, A.K. Pani and Sangita Yadav (2013), Optimal error estimates of two mixed finite element methods for parabolic integro-difierential equations with nonsmooth initial data, J.Sci. Comp.,56, 131-164.

  5. * S. Yadav, A.K.Pani and E.J.Park (2013),Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations, Math. Comp., 82, pp. 1297-1335.

  6. S. Bajpai, N. Nataraj and A. K. Pani (2013), On fully discrete finite element schemes for equa- tions of motion of Kelvin-Voigt fluids, Intl.J. Numer. Anal. Modelling, 10, pp.481507

  7. Sangita Yadav, Amiya K. Pani and Neela Nataraj (2013), Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems, Journal of Scientific Computing, 54, 4576.

  8. S. Bajpai, N. Nataraj, A. K. Pani, P. Damazio and J. Y. Yuan (2013), Semidiscrete Galerkin method for equations of motion arising in Kelvin-Voigt model of viscoelastic fluid ow, Numer.Meth. PDE., 29, 857-883.

  9. * Sajid Memon, Neela Nataraj and Amiya K. Pani (2012), An Aposteriori Error Analysis of a Mixed Finite Element Galerkin Approximation to Second Order Linear Parabolic Problems SIAM J. Numer. Anal., 50, pp. 1367-1393.

  10. P. Danumjaya and A.K. Pani (2012), Mixed finite element methods for a fourth order reaction difiusion equation, Numer Meth PDE.,28, pp. 12271251.

  11. Deepjyoti Goswami and A.K.Pani (2011), An Alternate Approach to Optimal L2-error anal- ysis of semidiscrete Galerkin methods for linear parabolic problems with nonsmooth initial data,Numer. Funct. Anal. Optimz., 32, pp. 946-982.

  12. D. Pradhan,S. Baskar, Neela Nataraj and A.K. Pani (2011), A Robin-type Non-Overlapping Domain Decomposition Procedure for Second Order Elliptic Problems , Adv. Comput. Math. 34, pp. 339-368.

  13. * Deepjyoti Goswami and A. K. Pani ( 2011 ), A priori error estimates for semidiscrete finite element approximations to equations of motion arising in Oldroyd fuids of order one, International J. Numer. Anal and Modelling (IJNAM), 8, pp.324-352.

  14. * A.K. Pani and Sangita Yadav (2011), An hp-local discontinuous Galerkin method for parabolic integro-differential equations, J. Sci. Comp. 46, pp.71-99.

  15. *A. K. Pani, G. Fairweather and R.I. Fernandes (2010), ADI Orthogonal Spline Collocation Methods for Parabolic Integro-Differential Equations , IMA J Numer Anal. 30, pp. 248-276.

  16. Nupur Gupta, Neela Nataraj and A.K. Pani (2010), On the optimal control problem of laser surface hardening, Internl. J. Numer Anal. Model, 7, pp. 667-680.

  17. Sarvesh Kumar,Neela Nataraj and A. K. Pani (2009), Discontinuous Galerkin finite volume methods for second order linear elliptic problems, Numer. Meth. PDEs.25, pp.1402-1424.

  18. * T. Gudi, Neela Nataraj and A. K. Pani (2009), On L2-Error Estimate for Non-Symmetric Interior Penalty Galerkin Approximation to Linear Elliptic Problems with Nonhomogeneous Dirichlet Data, J. Comput. Appl. Math.228,pp.30-40.

  19. * T. Gudi, Neela Nataraj and A. K. Pani (2008), A mixed discontinuous Galerkin method for the biharmonic equation, J. Scientific Computing. 37,pp.139-161.

  20. A.K. Patel, A.K. Pani and Neela Nataraj (2008 ) A mortar element method for parabolic problems, Numer. Meth. PDEs.24,pp.1460-1484.

  21. * T. Gudi, Neela Nataraj and A. K. Pani (2008), hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems, Numer. Math.109, pp.233-268.

  22. * A. K. Pani, Graeme Fairweather and Ryan Fernandes (2008), Alternate Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a positive type memory term, SIAM J. Numer. Anal.46, pp. 344-364.

  23. D. Pradhan, A.K. Pani and Neela Nataraj ( 2008 ), An explicit/implicit Galerkin domain decomposition procedure for parabolic integro-difierential equations,J Appl. Math. Comp.28, pp. 295-311.

  24. * T. Gudi, Neela Natraj and A. K. Pani ( 2008 ), An hp-local discontinuous Galerkin method for some quasi-linear elliptic boundary value problems of non-monotone type , Math. Comp. 77, pp. 731-756.

  25. Sarvesh Kumar, Neela Natraj and A. K. Pani (2008),Finite volume element method for second order hyperbolic equations, Intnl.J . Numer. Anal and Modeling.5 , pp. 132-151.

  26. Pritam Mantri, Neela Natraj and A.K. Pani (2008), A quolocation method for Burgers' equation, J. Comp. Math. Appl. 213, pp. 1-13.

  27. * Anil Kumar, M. C. Joshi and A. K. Pani (2007), On Approximation Theorems for Control- lability of Non-linear Parabolic Problems, IMA J. Math. Control Info.24, pp.115-136.

  28. * T. Gudi and A. K. Pani (2007), Discontinuos Galerkin Methods for Quasilinear Elliptic Problems on Nonmonotone Type, SIAM J. Numer Anal. 45, pp. 163-192.

  29. * J. Agarwal. Kannan Moudgalya and A. K. Pani (2006), Sliding Motion of Discontinuous Dynamical Systems Described by Semi-Implicit Index One Difierential Algebraic Equations, 61 , pp. 4722-4731, Chemical Engineering Science.

  30. * A. K. Pani, Jin Yun Yuan and Pedro D. Damazio (2006), Linearized Backward Euler Method for the Equations of Motion Arising on the Oldroyd Model, SIAM J. Numer. Anal. 44, pp. 804-825 .

  31. P. Dhanumjaya and A. K. Pani ( 2006), Numerical methods for the extended Fisher-Kolmogorov Equation, International J. Numer. Anal. and Modeling, 6, pp. 186-210.

  32. * A. K. Pani and Jin Yun Yuan (2005), Semidiscrete finite element Galerkin approximation to the equations of motion arising in the Oldroyd model, IMA J. Numer. Anal. 25, pp. 750-782.

  33. Pradeepa Nair and A. K. Pani (2005), Finite Element Approximation to a Class of Viscoelastic Problems with Short Memory under Conditions of Friction, Dynamics of Continuous, Discrete and Impulsive Systems, Ser. B: Appl. & Algorithm, 12, pp. 360-380.

  34. * L Jones Doss and A. K. Pani (2005), A quolocation method for unidimensional single phase Stefan problem, IMA J. Numer. Anal. 25, pp. 139-159

  35. P. Dhanumjaya and A. K. Pani (2005), Orthogonal cubic spline collocation method for the extended Fisher-Kolmogorov equation, Journal of Computational and Applied Mathematics , 174, pp. 101-117.

  36. A. K. Pani and Sang K. Chung (2004), A second order splitting lumped mass finite element method for the Rosenau equation, Differential Equations and Dynamical Systems, 12 (2004), pp. 331-351.

  37. * Jyoti Agarwal, Kannan M. Moudgalya and A. K. Pani (2004), Sliding motion and stability of a class of discontinuous dynamical systems, Nonlinear Dynamics, 37, pp. 151-168.

  38. S. Arul Veda Manickam, Kannan M. Moudgalya and A. K. Pani (2004), Higher order fully dis- crete scheme combined with H1-Galerkin mixed finite element method for semilinear reaction- diffusion equations, J. Applied Mathematics and Computing, 15, pp. 1-28.

  39. Rajen K. Sinha, Ajay K. Otta and A. K. Pani (2004), An H1-Galerkin mixed method for second order hyperbolic equations, International J. Numer. Anal and Modeling, 1, pp. 111- 130.

  40. Rajen K. Sinha, A. K. Pani and Sang K. Chung (2003), The effect of spatial quadrature on the semidiscrete finite element Galerkin method for a strongly damped wave equation, Number Funct. Anal and Optimiz. 24, no. 3-4, pp. 311-325./li>
  41. Pradeepa Nair and A. K. Pani (2003), Finite element methods for parabolic variational in- equalities with a Volterra term,Numer Funct. anal & Optimize. 24, pp. 107-127.

  42. * A. K. Pani and Graeme Fairweather (2002), An H1-Galerkin mixed finite element method for an evolution equation with a positive type memory term, SIAM J. Numer. Anal. 40, pp. 1475-1490.

  43. * A. K. Pani and Gareme Fairweather (2002), H1Galerkin mixed finite element methods for parabolic integro-differential equations, IMA J. Numer. Anal. 22, pp. 231{252.

  44. * A. K. Pani and Sang K. Chung (2001), Numerical methods for the Rosenau equation, Applicable Analysis, 77, pp. 351-369.

  45. * Rajen K. Sinha and A. K. Pani (2001), Finite element approximation with quadrature to a time dependent parabolic integro-differential equations with non smooth initial data, J. Integral Equations and Appl.13, pp. 35-72.

  46. A. K. Pani and Jin Yun Yuan (2001), Mixed finite element method for the strongly damped wave equation, Numer. Meth. PDE, 17, pp.105{119.

  47. * Rajen K. Sinha and A. K. Pani (2000), Error estimates for semidiscrete Galerkin method for time dependent parabolic integro-differential equations with non smooth data, CALCOLO: A Quarterly on Numerical Analysis and Theory of Computation, Springer Verlag Publ., 37, pp. 181{205.

  48. * A. K. Pani (1999), A qualocation method for parabolic partial differential equations, IMA J. Numer. Anal. 19, pp. 473{495.

  49. * Rajen K. Sinha and A. K. Pani (1998), The effect of spatial quadrature on finite element Galerkin approximation to a hyperbolic integro-differential equations, Numer. Funct. Anal. & Optimz. , 19, pp. 1129{1153.

  50. Arul Veda Manickam, Sang K. Chung and A. K. Pani (1998), A second order splitting com- bined with cubic spline orthogonal collocation method for the Rosenau equation, Numer. Meth. PDE. 14, pp. 695{716.

  51. * Rajen K. Sinha and A. K. Pani (1998), On the backward Euler method for time dependent parabolic integro-differential equations with non smooth initial data, J. Integral Equations and Appl. 10, pp. 219{249.

  52. * Rajen K. Sinha and A. K. Pani (1998), Quadrature based finite element approximation to time dependent parabolic equations with non smooth initial data, CALCOLO: A Quarterly on Numerical Analysis and Theory of Computation, 35, pp. 225{248, Springer Verlag Publ.

  53. M. A. Mohammed Ali and A. K. Pani (1998), An H1-Galerkin mixed finite element method combined with the modified method of characteristics for incompressible miscible displacement problems in porous media, Differential Equations and Dynamical Systems 6, pp. 77{85.

  54. * A. K. Pani (1998), An H1-Galerkin mixed finite element method for parabolic partial dif- ferential equations, SIAM J. Numer. Anal. 35, pp. 712{727.

  55. Arul Veda Manickam, Kannan . Moudgalya and A. K. Pani (1998), A second order split- ting combined with cubic spline orthogonal collocation method for the Kuramoto- Sivashinsky equation, Computers & Mathematics with Applications, 35, pp. 5{25.

  56. * A. K. Pani, T Sengadir and D. V. Pai (1997), A Leray Schauder type theorem and its applications to neutral functional differential equations, Nonlinear Analysis TMA, 28, pp. 701-720.

  57. Jones T. Doss, S. Padhy and A. K. Pani (1997), A priori L2-error estimates for a Stefan-type problem in one space dimension, Numer. Meth. PDEs., 13, pp. 393-416.

  58. S. K. Chung, M. G. Park and A. K. Pani (1997), Convergence of finite difference method for the generalized solutions of Sobolev equations,J. Korean Math. Soc., 34, pp. 515-532.

  59. * Haritha Saranga and A. K. Pani (1997), Finite element Galerkin method for the `good' Boussinesq equation, Nonlinear Analysis: TMA, 29, pp. 937-956.

  60. T. Sengadir and A. K. Pani (1996), Weak solutions of integro-differential and functional differential equations, Differential Equations and Dynamical Systems 4, 411-422.

  61. * A.K. Pani and Todd E. Peterson (1996), Finite element methods with numerical quadrature for parabolic integro-differential equations, SIAM J. Numer. Anal., 33, pp. 1084-1105

  62. Rajen K. Sinha and A. K. Pani (1996), Negative norm estimates and super convergence results for parabolic integro-differential equations, J. Integral Equations and Appl., 8, pp. 65-98.

  63. S. K. Chung and A. K. Pani (1995), On the convergence of finite difference schemes for generalized solutions of Sobolev equations, J. Korean Math. Soc., 32, pp. 815-834.

  64. L Jones T. Doss and A. K. Pani (1995), On super convergence results and negative norm estimates for a unidimensional single phase Stefan problem, Numer. Functional Anal. & Opt., 16, pp. 153-175.

  65. T. Sengadir and A. K. Pani (1994), Topological Transversality: applications to second order integro-differential and functional differential equations, Bull. Austral. Maths. Soc. 49, 251-264.

  66. A. K. Pani (1993), A finite element method for a diffusion problem with constrained energy and nonlinear boundary conditions, J. Austral. Math. Soc. Ser B, 35, pp. 87-102.

  67. * A. K. Pani, V. Thomee and L. B. Wahlbin (1992), Numerical methods for hyperbolic and parabolic integro-differential equations, J. Integral Equations & Applications, 4, pp. 533-584.

  68. A. K. Pani and P. C. Das (1991), A finite element method for a single-phase semilinear Stefan problem in one space dimension, Numer. Funct. Anal. & Optimiz., 12 (1991), pp. 153-171.23

  69. * A. K. Pani and P. C. Das (1991), A priori error estimates for a single-phase quasilinear Stefan problem in one space dimension, IMA J. Numer. Anal., 11, pp. 377-392.

  70. * A. K. Pani and P. C. Das (1991), A finite element Galerkin method for a unidimensional single-phase nonlinear Stefan problem with Dirichlet boundary conditions IMA J. Numer. Anal., 11, pp. 99-113.

  71. D. Bhaguna, V. Raghavendra and A. K. Pani (1990), Rothe's method to semilinear hyperbolic integro-differential equations, J. Appl. Math. & Stoch. Anal., 3, pp. 245-252.

  72. * A. K. Pani and P. C. Das (1989), A priori error estimates in H1 and H2-norms for Galerkin approximations to a single phase nonlinear Stefan problem in one space dimension, IMA J. Numer. Anal., 9, pp. 213-229.

  73. A. K. Pani and P. C. Das (1987), An H1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form, Internatl. J. Math. & Math. Sci., 10, pp. 35-360.