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Numerical Resolution Near t = 0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1

Published online by Cambridge University Press:  20 August 2015

Qingshan Chen ,
Zhen Qin  and
Roger Temam
Qingshan Chen*
Affiliation:
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306, USA
Zhen Qin*
Affiliation:
Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA
Roger Temam*
Affiliation:
Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA
*
Email:qchen3@fsu.edu
Email:qinz@indiana.edu
Corresponding author.Email:temam@indiana.edu
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Abstract

The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical scheme in use. Applications of the remedy procedures to the 1D viscous Burgers equation, and to the 1D nonlinear reaction-diffusion equation are presented. The remedy procedures are applicable to other nonlinear diffusion equations as well.

Keywords

35B6535K5535K5765M2065M60Compatibility conditionscorner singularitiesviscous Burgers equationnonlinear convection diffusion equationfinite element methods
Type
Research Article
Information
Communications in Computational Physics , Volume 9 , Issue 3 , March 2011 , pp. 568 - 586
Copyright
Copyright © Global Science Press Limited 2011

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