A Posteriori Error Estimates for Lumped Mass Finite Element Method for Linear Parabolic Problems Using Elliptic Reconstruction. (2nd December 2017)

• Record Type: Journal Article
• Authors: Gupta, Jhuma Sen; Sinha, Rajen Kumar
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 12(2017)
• Page Start: 1527
• Page End: 1547
• Publication Date: 2017-12-02
• Subjects: A posteriori error estimates -- elliptic reconstruction -- lumped mass finite element approximation -- parabolic problems; 65M60 -- 65M15 -- 65N15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1338730
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We 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 ℝ 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 (Ω). The a posteriori error estimates we derive are optimal order in both the and -norms.