Volume 9, Issue 3
Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1

Qingshan Chen, Zhen Qin & Roger Temam

Commun. Comput. Phys., 9 (2011), pp. 568-586.

Published online: 2011-03

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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.

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@Article{CiCP-9-568, author = {}, title = {Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1}, journal = {Communications in Computational Physics}, year = {2011}, volume = {9}, number = {3}, pages = {568--586}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.110909.160310s}, url = {http://global-sci.org/intro/article_detail/cicp/7511.html} }
TY - JOUR T1 - Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1 JO - Communications in Computational Physics VL - 3 SP - 568 EP - 586 PY - 2011 DA - 2011/03 SN - 9 DO - http://doi.org/10.4208/cicp.110909.160310s UR - https://global-sci.org/intro/article_detail/cicp/7511.html KW - AB -

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.

Qingshan Chen, Zhen Qin & Roger Temam. (2020). Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1. Communications in Computational Physics. 9 (3). 568-586. doi:10.4208/cicp.110909.160310s
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