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A New Discontinuous Galerkin Method for Parabolic Equations with Discontinuous Coefficient

Published online by Cambridge University Press:  28 May 2015

Rongpei Zhang ,
Xijun Yu ,
Xia Cui ,
Xiaohan Long  and
Tao Feng
Rongpei Zhang*
Affiliation:
School of Sciences, Liaoning Shihua University, Fushun 113001, Liaoning, China
Xijun Yu*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Xia Cui*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Xiaohan Long*
Affiliation:
School of Mathematics and Information, Ludong University, Yantai 264025, Shandong, China
Tao Feng*
Affiliation:
National Key Laboratory of Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
*
Corresponding author.Email address:rongpeizhang@163.com
Corresponding author.Email address:yuxj@iapcm.ac.en
Corresponding author.Email address:cui_xia@iapcm.ac.cn
Corresponding author.Email address:long669@163.com
Corresponding author.Email address:fengtao2@mail.ustc.edu.cn
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Abstract

In this paper, a new discontinuous Galerkin method is developed for the parabolic equation with jump coefficients satisfying the continuous flow condition. Theoretical analysis shows that this method is L2 stable. When the finite element space consists of interpolative polynomials of degrees k, the convergent rate of the semi-discrete discontinuous Galerkin scheme has an order of . Numerical examples for both 1-dimensional and 2-dimensional problems demonstrate the validity of the new method.

Keywords

65M6035K05Parabolic equationdiscontinuous coefficientdiscontinuous Galerkin methoderror estimatestability analysis
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 325 - 342
Copyright
Copyright © Global Science Press Limited 2013

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