Published Papers in Journals:
- 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).
- 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).
- 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.
- 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.
- * S. Yadav, A.K.Pani and E.J.Park (2013),Superconvergent discontinuous Galerkin methods
for nonlinear elliptic equations, Math. Comp., 82, pp. 1297-1335.
- 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
- 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.
- 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.
- * 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.
- P. Danumjaya and A.K. Pani (2012), Mixed finite element methods for a fourth order reaction
difiusion equation, Numer Meth PDE.,28, pp. 12271251.
- 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.
- 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.
- * 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.
- * 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.
- *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.
- 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.
- 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.
- * 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.
- * 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.
- A.K. Patel, A.K. Pani and Neela Nataraj (2008 ) A mortar element method for parabolic
problems, Numer. Meth. PDEs.24,pp.1460-1484.
- * 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.
- * 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.
- 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.
- * 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.
- 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.
- Pritam Mantri, Neela Natraj and A.K. Pani (2008), A quolocation method for Burgers' equation, J. Comp. Math. Appl. 213, pp. 1-13.
- * 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.
- * 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.
- * 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.
- * 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 .
- 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.
- * 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.
- 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.
- * 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
- 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.
- 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.
- * 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.
- 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.
- 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.
- 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>
- 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.
- * 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.
- * 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.
- * A. K. Pani and Sang K. Chung (2001), Numerical methods for the Rosenau equation,
Applicable Analysis, 77, pp. 351-369.
- * 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.
- 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.
- * 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.
- * A. K. Pani (1999), A qualocation method for parabolic partial differential equations, IMA
J. Numer. Anal. 19, pp. 473{495.
- * 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.
- 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.
- * 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.
- * 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.
- 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.
- * 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.
- 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.
- * 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.
- 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.
- 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.
- * Haritha Saranga and A. K. Pani (1997), Finite element Galerkin method for the `good'
Boussinesq equation, Nonlinear Analysis: TMA, 29, pp. 937-956.
- T. Sengadir and A. K. Pani (1996), Weak solutions of integro-differential and functional
differential equations, Differential Equations and Dynamical Systems 4, 411-422.
- * 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
- 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.
- 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.
- 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.
- 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.
- 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.
- * 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.
- 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
- * 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.
- * 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.
- 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.
- * 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.
- 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.