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

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

2010-11-20

arxiv.org/abs/1011.4549v1

First published in Comm. Comp. Phys., 9(3):568-586, March 2011. Published by Global Science Press

Mathematics

Numerical Analysis

Scientific paper

10.4208/cicp.110909.160310s

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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