A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems
type: Item
instance of: scholarly article
title: A posteriori error analysis of the discontinuous finite element methods for first order hyperbolic problems
zbMATH Open document ID: 1242.65187
author: Tie Zhang
author: Nan Feng
published in: Applied Mathematics and Computation
publication date: 2011-12-29T00:00:00Z
review text: The authors propose an a posteriori error analysis method for discontinuous Galerkin finite element approximations (DG) for steady and nonsteady first-order hyperbolic scale equations. Several residual-based a posteriori error estimators for the steady problem are constructed that provide global upper bounds on the error in DG-, \(L_2\)- and \(H^{-1}\)-norms, and local lower bounds on the error in \(L_2\)-norm. For the nonsteady problem the authors discretize the problem by employing an implicit Euler time scheme with space DG. The derived a posteriori error estimators yield the global upper bound on the error in \(L_\infty(0,T;L_2)\).
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35L40
zbMATH DE Number: 5992874
zbMATH Keywords: a posteriori error analysis
zbMATH Keywords: discontinuous Galerkin finite element approximation
zbMATH Keywords: first-order hyperbolic scale equations
zbMATH Keywords: implicit Euler time scheme
reviewed by: Vladimir L. Makarov
MaRDI profile type: Publication
full work available at URL: j.amc.2011.06.059
OpenAlex ID: W1973000602
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DOI: 10.1016/J.AMC.2011.06.059
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description: scientific article; zbMATH DE number 5992874