A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations

A Godunov-mixed finite element method on changing meshes is presented to simulate the nonlinear Sobolev equations. The convection term of the nonlinear Sobolev equations is approximated by a Godunov-type procedure and the diffusion term by an expanded mixed finite element method. The method can simu...

Full description

Bibliographic Details
Main Author:	Tongjun Sun
Format:	Article
Language:	English
Published:	Hindawi Limited 2012-01-01
Series:	Abstract and Applied Analysis
Online Access:	http://dx.doi.org/10.1155/2012/413718

id	doaj-c542a365321048728b439ecebefa2067
record_format	Article
spelling	doaj-c542a365321048728b439ecebefa20672020-11-24T22:18:15ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/413718413718A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev EquationsTongjun Sun0School of Mathematics, Shandong University, Jinan 250100, ChinaA Godunov-mixed finite element method on changing meshes is presented to simulate the nonlinear Sobolev equations. The convection term of the nonlinear Sobolev equations is approximated by a Godunov-type procedure and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Almost optimal error estimates in L2-norm under very general changes in the mesh can be obtained. Finally, a numerical experiment is given to illustrate the efficiency of the method.http://dx.doi.org/10.1155/2012/413718
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Tongjun Sun
spellingShingle	Tongjun Sun A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations Abstract and Applied Analysis
author_facet	Tongjun Sun
author_sort	Tongjun Sun
title	A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
title_short	A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
title_full	A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
title_fullStr	A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
title_full_unstemmed	A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations
title_sort	godunov-mixed finite element method on changing meshes for the nonlinear sobolev equations
publisher	Hindawi Limited
series	Abstract and Applied Analysis
issn	1085-3375 1687-0409
publishDate	2012-01-01
description	A Godunov-mixed finite element method on changing meshes is presented to simulate the nonlinear Sobolev equations. The convection term of the nonlinear Sobolev equations is approximated by a Godunov-type procedure and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Almost optimal error estimates in L2-norm under very general changes in the mesh can be obtained. Finally, a numerical experiment is given to illustrate the efficiency of the method.
url	http://dx.doi.org/10.1155/2012/413718
work_keys_str_mv	AT tongjunsun agodunovmixedfiniteelementmethodonchangingmeshesforthenonlinearsobolevequations AT tongjunsun godunovmixedfiniteelementmethodonchangingmeshesforthenonlinearsobolevequations
_version_	1725782648826101760

A Godunov-Mixed Finite Element Method on Changing Meshes for the Nonlinear Sobolev Equations

Similar Items