Numerical Resolution Near t=0 of Nonlinear Evolution Equations in the Presence of Corner Singularities in Space Dimension 1 (Communications in Computational Physics, 2011)
The incompatibilities between the initial and boundary data will cause singularitiesat the time-space corners, which in turn adversely affect the accuracy of thenumerical schemes used to compute the solutions. We study the corner singularity issuefor nonlinear evolution equations in 1D, and propose two remedy procedures thateffectively recover much of the accuracy of the numerical scheme in use. Applicationsof the remedy procedures to the 1D viscous Burgers equation, and to the 1D nonlinearreaction-diffusion equation are presented. The remedy procedures are applicable toother nonlinear diffusion equations as well.