\(L^2\)-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations
type: Item
instance of: scholarly article
title: \(L^2\)-error analysis of discontinuous Galerkin approximations for nonlinear Sobolev equations
zbMATH Open document ID: 1273.65126
author: Yanyan Li
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2013-03-15T00:00:00Z
review text: The authors apply a discontinuous Galerkin method with symmetric interior penalty terms to approximate the solution of nonlinear Sobolev equations. They introduce an appropriate elliptic type projection of the solution of a Sobolev equation and prove its optimal convergence. Finally, a semidiscrete approximation of the solutions of nonlinear Sobolev differential equations is constructed, and their convergence in \(L^2\) normed space with optimal order of convergence is proved.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M20
zbMATH DE Number: 6145355
zbMATH Keywords: nonlinear Sobolev equations
zbMATH Keywords: \(L^2\)-error estimation
zbMATH Keywords: discontinuous Galerkin approximations
zbMATH Keywords: symmetric interior penalty method
zbMATH Keywords: semidiscretization
reviewed by: Qin Meng Zhao
MaRDI profile type: Publication
full work available at URL: s13160-012-0096-7
OpenAlex ID: W2049386108
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DOI: 10.1007/S13160-012-0096-7
description: scientific article; zbMATH DE number 6145355