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Publications

 

  • R. Manohar and R.K. Sinha, Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems, J. Comp. Math., 40 (2022), pp. 147 -176.

 

  •  R. Manohar and R.K. Sinha, Local a posteriori error analysis of finite element method for parabolic boundary control problems, J. Scientific Computing, 91 (2022), no. 1, Paper No. 17, pp. 1 - 43.

 

  •  R. Manohar and R.K. Sinha, Local a posteriori error estimates for boundary control problems governed by nonlinear parabolic equations, J. Comput. Appl. Math. 409 (2022), Paper No. 114146, pp. 1 - 29.

 

  •  R. Manohar and R.K. Sinha, A posteriori L∞(L∞)-error estimates for finite-element approximations to parabolic optimal control problems, Comput. Appl. Math., 40 (2021), no. 8, Paper No. 298, pp. 1 - 31.

 

  •  R. Manohar and R.K. Sinha, A posteriori error estimates for parabolic optimal control problems with controls acting on lower dimensional manifolds, J. Scientific Computing, 89 (2021), no. 2, pp. 1 -  34.

 

  •  P. Shakya and R.K. Sinha, Finite element approximations of parabolic optimal control problem with measure data in time, Appl. Anal., 100 (2021), no. 12, pp. 2706 - 2734.

 

  •  S. Mahata and R.K. Sinha, Finite element method for fractional parabolic integro-differential equations with smooth and nonsmooth initial data, J. Scientific Computing, 87 (2021), no. 1, Paper No. 7, pp. 1 - 32.

 

  •  T. Ray and R.K. Sinha, An adaptive finite element method for parabolic interface problems with nonzero flux jumps, Comput. Math. Appl., 82 (2021), pp. 97 - 112.

 

  • S. Mahata and R.K. Sinha, On the existence, uniqueness and stability results for time-fractional parabolic integrodifferential equations, J. Integral Equations Appl., 32 (2020), no. 4, pp. 457 - 477.

 

  • R. Manohar and R.K. Sinha, Space-time a posteriori error analysis of finite element approximation for parabolic optimal control problems: a reconstruction approach, Optimal Control Appl. Methods 41 (2020), no. 5, pp. 1543 - 1567.

 

  • T. Pramanick and R.K. Sinha, Composite finite element approximation for parabolic problems in nonconvex polygonal domains, Comput. Methods Appl. Math., 20 (2020), no. 2, pp. 361 - 378.

 

  • 43. T. Ray and R.K. Sinha, An adaptive finite element method for semilinear parabolic interface problems with nonzero flux jump, Appl. Numer. Math., 153 (2020), pp. 381 - 398. 

 

  • P. Shakya and R.K. Sinha, A priori error estimates for finite element discretizations of parabolic optimal control problems with measure data, Numer. Funct. Anal. Optim., 41 (2020), no. 2, pp. 158 - 191.

 

  • P. Shakya and R.K. Sinha, Finite element method for parabolic optimal control problems with a bilinear state equation, J. Comput. Appl. Math. 367 (2020), pp. 1 - 26.

 

  • T. Pramanick and R.K. Sinha, Error estimates for two-scale composite finite element approximations of parabolic equations with measure data in time for convex and nonconvex polygonal domains, Appl. Numer. Math., 143 (2019), pp. 112 - 132.

 

  • G.M.M. Reddy, R.K. Sinha and J. A. Cuminato, A posteriori error analysis of the Crank-Nicolson finite element method for parabolic integro-differential equations, J. Scientific Computing, 79 (2019), no. 1, pp. 414 - 441.

 

  •  P. Shakya and R.K. Sinha, A prior and a posteriori error estimates of finite-element approximations for elliptic optimal control problem with measure data, Optimal Control Appl. Methods, 40 (2019), no. 2, pp. 241 - 264.

 

  • P. Shakya and R.K. Sinha, A posteriori error analysis for finite element approximations of parabolic optimal control problems with measure data, Appl. Numer. Math., 136 (2019), pp. 23 - 45

 

  •  T. Pramanick and R.K. Sinha, Composite finite element approximation for nonlinear parabolic problems in nonconvex polygonal domains, Numer. Methods Partial Differential Equations, 34 (2018), no. 6, pp. 2316 - 2335.

 

  •  T. Pramanick and R.K. Sinha, Two-scale composite finite element method for parabolic problems with smooth and nonsmooth initial data, J. Appl. Math. Comput., 58 (2018), no. 1-2, pp. 469 - 501.

 

  •  J. Sen Gupta, R.K. Sinha, G.M.M. Reddy and J. Jain, A posteriori error analysis of the Crank-Nicolson finite element method for linear parabolic interface problems: a reconstruction approach, J. Comput. Appl. Math. 340 (2018), pp. 173 - 190.

 

  •  J. Sen Gupta and R.K. Sinha, A posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction, Appl. Anal., 97 (2018), no. 4, pp. 552 - 570.

 

  • J. Sen Gupta and R.K. Sinha, A posteriori error estimates for lumped mass finite element method for linear parabolic problems using elliptic reconstruction, Numer. Funct. Anal. Optim., 38 (2017), no. 12, pp. 1527 - 1547.

 

  •  P. Shakya and R.K. Sinha, A priori and a posteriori error estimates of H1-Galerkin mixed finite element method for parabolic optimal control problems, Optimal Control Appl. Methods, 38 (2017), no. 6, 1056 - 1070.

 

  •  J. Sen Gupta, R.K. Sinha, G.M.M. Reddy and J. Jain, New interpolation error estimates and a posteriori error analysis for linear parabolic interface problems, Numer. Methods Partial Differential Equations, 33 (2017), no. 2, pp. 570 - 598.

 

  •  J. Sen Gupta, R.K. Sinha, G.M.M. Reddy and J. Jain, A posteriori error analysis of two-step backward differentiation formula finite element approximation for parabolic interface problems, J. Scientifc Computing, 69 (2016), no. 1, pp. 406 - 429.

 

  • G. M. M. Reddy and R. K. Sinha, The Backward Euler A posteriori Anisotropic Error Analysis for Parabolic Integro-Differential Equations, Numerical Methods Partial Differential Equations, 32 (2016), no. 5, pp. 1309 - 1330.

 

  • G. M. M. Reddy and R. K. Sinha, On the Crank-Nicolson Anisotropic A posteriori Error Analysis for Parabolic Integro-Differential Equations, Mathematics of Computation, 85 (2016), no. 301, pp. 2365 - 2390.

 

  • G. M. M. Reddy and R. K. Sinha, Ritz-Volterra reconstructions and a posteriori error analysis of finite element method for parabolic integro-differential equations, IMA J. Numer. Anal., 35 (2015), no. 1, pp. 341-371.

 

  • M Tripathy and R.K Sinha, Convergence of H1-Galerkin mixed finite element method for parabolic problems with reduced regularity on Initial data, Numerical Analysis and Applications, 7 (2014), no. 3, 227 - 240.

 

  • M. Tripathy and R.K. Sinha, A posteriori error estimates for H1 -Galerkin mixed finite-element method for parabolic problems, Appl. Anal. 92 (2013), no. 4, pp. 855 - 868.

 

  • B. Deka, Sinha, R. K. Sinha, R. C. Deka, T. Ahmed, Finite element method with quadrature for parabolic interface problems, Neural Parallel Sci. Comput., 21 (2013), no. 3-4, 477 - 496.

 

  • B. Deka and R. K. Sinha, Finite Element Methods for Second-Order Linear Hyperbolic Interface Problems, Appl. Math. Comput.,  218(22), 2012, pp. 10922 - 10933.

 

  • M. Tripathy and R. K. Sinha, Superconvergence of H-Galerkin Mixed Finite Element  Methods for Second-Order Elliptic Equations, Numer. Funct. Anal. & Optim, , 33(3), 2012, pp. 320 - 337.

 

  • B. Deka and R. K. Sinha, L(L2) and L(H1) - Norms Error Estimates in Finite Element for Linear Parabolic Interface Problems, Numer. Funct. Anal. & Optim, , 32(3), 2011, pp. 267 - 285.

 

  •  R. K. Sinha, R. E. Ewing and R. D. Lazarov, Mixed Finite Element Approximations of Parabolic Integro-Differential Equations with Nonsmooth Initial Data, SIAM J. Numer. Anal., 47(5), 2009,  pp. 3269 - 3292.

 

  • M. Tripathy and R. K. Sinha, Superconvergence of $H^1$-Galerkin Mixed Finite Element Method for Parabolic Problems, Applicable Analysis, 88 (2009), pp. 1213 - 1231.

 

  • R. K. Sinha and B. Deka, Finite element methods for semilinear elliptic and parabolic interface problems, Appl. Numer. Math., 59 (2009), 1870 - 1883

 

  • R. K. Sinha and B. Deka, An unfitted finite element method for elliptic and parabolic interface problems, IMA J. Numer. Anal., 27(3), 2007, pp. 529 - 549.

 

  • R. K. Sinha and Jurgen Geiser, Error estimates for finite volume element methods for convection-diffusion-reaction equations, Appl. Numer. Math., 57(1), 2007, pp. 59 - 72.

 

  • R. K. Sinha and B. Deka, A priori error estimates in finite element method for nonselfadjoint elliptic and parabolic interface problems, Calcolo, 43, 2006, pp. 253 - 278.

 

  •   R. K. Sinha, R. E. Ewing and R. D. Lazarov, Some new error estimates of a semidiscrete finite volume element method for parabolic integro-differential equation with nonsmooth initial data, SIAM J. Numer. Anal., 43 (2006), no. 6, pp. 2320-2343.

 

  • R. K. Sinha and B. Deka, On the convergence of finite element method for elliptic interface problems, Numer. Funct. Anal. & Optim, 27 (2006), no. 1, pp. 99 - 115.

 

  • R. K. Sinha and B. Deka, Optimal error estimates for linear parabolic problems with discontinuous coefficients, SIAM J. Numer. Anal., 43 (2005), no. 2, pp. 733-749.

 

  • R. K. Sinha and R. D. Lazarov, A new technique for error analysis of finite element approximations of parabolic problems with nonsmooth initial data, Approximation Theory; Academy Publishing House, 2004, 296-308.

 

  •  A. K. Pani, R. K. Sinha and A. K. Otta, An H^1-Galerkin mixed method for second order hyperbolic equations, Int. J. Numer. Anal. Model., 1  (2004),  no. 2, 111--130.

 

  • A. K. Pani, R. K. Sinha and S. K. Chung, The effect of spatial quadrature on the semidiscrete finite element Galerkin method for a strongly damped wave equation, Numer. Funct. Anal. & Optimiz., 24 (2003), no.3-4, 311--325.

 

  •  R. K. Sinha, Finite element approximations with quadrature for second-order hyperbolic equations, Numer. Methods Partial Differential Equations, 18 (2002), no. 4, 537--559.

 

  • A. K. Pani and R. K. Sinha, Finite element approximation with quadrature to a time dependent parabolic integro-differential Equation with nonsmooth  initial data,  J. Integral Equations & Applications, 13 (2001),  35--72.

 

  • A. K. Pani and R. K. Sinha, Error estimates for semidiscrete Galerkin approximation to a time dependent parabolic integro-differential equations with nonsmooth data, Calcolo, 37 (2000), 181--205.

 

  • R. K. Sinha and A. K. Pani, The effect of spatial quadrature on finite element Galerkin approximations to hyperbolic integro differential equations, Numer. Funct. Anal. & Optimiz., 19 (1998), 1129--1153.

 

  • A. K. Pani and R. K. Sinha, On the backward Euler method for time dependent parabolic integro-differential equation with nonsmooth initial data, J. Integral Equations  & Applications, 10 (1998), 219--249.

 

  •  A. K. Pani and R. K. Sinha, Quadrature based finite element approximation to time dependent parabolic equations with nonsmooth initial data,  Calcolo, 35 (1998), 225--248.

 

  • A. K. Pani and R. K. Sinha, On superconvergence results and negative norm estimates for parabolic integro-differential equations, J. Integral Equations & Applications, 8 (1996), 65--98.