Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case
type: Item
instance of: scholarly article
title: Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case
zbMATH Open document ID: 1064.65082
author: Mats G. Larson
author: A. Jonas Niklasson
published in: Numerische Mathematik
publication date: 2005-02-08T00:00:00Z
review text: This paper deals with the properties of discontinuous Galerkin methods for elliptic problems in one spatial dimension. The analysis is based on a splitting of the discrete space into a direct sun of continuous piecewise polynomials and a space representing the discontinuous part of the functions also satisfying a special orthogonality relation. The authors prove stability results and \(L^2\) error estimates. Finally, some remarks on the elementwise conservative nature of the discontinuous Galerkin method are presented.
reviewed by: Pavol Chocholatý
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 2132205
zbMATH Keywords: stability
zbMATH Keywords: error estimates
zbMATH Keywords: discontinuous Galerkin methods
zbMATH Keywords: elliptic problems
MaRDI profile type: Publication
full work available at URL: s00211-004-0528-7
OpenAlex ID: W1972960967
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DOI: 10.1007/S00211-004-0528-7
description: scientific article; zbMATH DE number 2132205