Browsing by Author "Sen Gupta, Jhuma"
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- ItemA posteriori error analysis of semilinear parabolic interface problems using elliptic reconstruction(2018) Sen Gupta, Jhuma; Sinha, Rajen Kumar
- ItemA Posteriori Error Analysis of Two-Step Backward Differentiation Formula Finite Element Approximation for Parabolic Interface Problems(SPRINGER/PLENUM PUBLISHERS, 2016) Sen Gupta, Jhuma; Sinha, Rajen K.; Reddy, G. M. M.; Jain, JinankThis paper studies a residual-based a posteriori error estimates for linear parabolic interface problems in a bounded convex polygonal domain in . We use the standard linear finite element spaces in space which are allowed to change in time and the two-step backward differentiation formula (BDF-2) approximation at equidistant time step is used for the time discretizations. The essential ingredients in the error analysis are the continuous piecewise quadratic space-time BDF-2 reconstruction and Scott-Zhang interpolation estimates. Optimal order in time and an almost optimal order in space error estimates are derived in the -norm using only energy method. The interfaces are assumed to be of arbitrary shape but are smooth for our purpose. Numerical experiments are performed to validate the asymptotic behaviour of the derived error estimators.
- ItemA Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction(TAYLOR & FRANCIS INC, 2017) Sen Gupta, Jhuma; Sinha, Rajen KumarWe study residual-based a posteriori error estimates for both the spatially discrete and the fully discrete lumped mass finite element approximation for parabolic problems in a bounded convex polygonal domain in (2). In particular, the space discretization uses finite element spaces that are assumed to be nested one and the time discretization is based on the backward Euler approximation. The main key features used in the analysis are the reconstruction technique and energy argument combined with the stability of L-2 projection in H-1(). The a posteriori error estimates we derive are optimal order in both the -norms.