Energy norm a posteriori error estimation for discontinuous Galerkin methods.
type: Item
instance of: scholarly article
title: Energy norm a posteriori error estimation for discontinuous Galerkin methods.
zbMATH Open document ID: 1042.65083
DOI: 10.1016/S0045-7825(02)00593-5
author: Roland Becker
author: Peter Hansbo
author: Mats G. Larson
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2003-08-13T00:00:00Z
review text: The authors present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of dicontinuous Galerkin (dG) approximations of elliptic problems. The estimate is of optimal order and is valid for a general family of dG methods including the classical symmetric method of \textit{J. Nitsche} [Abh. Math. Semin. Univ. Hamburg 36, 9--15 (1971; Zbl 0229.65079)], the recent nonsymmetric method proposed by \textit{J. T. Oden, I. Babuška} and \textit{C. E. Baumann} [J. Comput. Phys. 146, 491--519 (1998; Zbl 0926.65109)], and stabilized versions thereof. The theory is developed for an elliptic problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. The illustrating numerical results indicate that the effectivity index is not severely effected by the fineness of the mesh.
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1963653
zbMATH Keywords: discontinuous Galerkin methods
zbMATH Keywords: error bounds
zbMATH Keywords: convergence
zbMATH Keywords: elliptic problems
reviewed by: Margit Lenard
MaRDI profile type: Publication
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full work available at URL: s0045-7825(02)00593-5
OpenAlex ID: W2026757688
description: scientific article; zbMATH DE number 1963653