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Numerical Experiments for a Singularly Perturbed Parabolic Problem with Degenerating Convective Term and Discontinuous Source

Carmelo Clavero, Jose L. Gracia, Grigorii Shishkin and Lidia Shishkina

Abstract

A finite difference scheme on special piecewise-uniform grids condensing in the interior layer is constructed for a singularly perturbed parabolic convection-diffusion equation with a discontinuous right-hand side and a multiple degenerating convective term (the convective flux is directed into the domain). When constructing the scheme, monotone grid approximations, similar to those developed and justified earlier by authors for a problem with a simple degenerating convective term, are used. Using the known technique of numerical experiments on embedded meshes, it is numerically verified that the constructed scheme converges ε-uniformly in the maximum norm at the convergence rate close to one.

Received: 2011-12-29
Revised: 2012-02-15
Accepted: 2012-02-20
Published Online: 2012
Published in Print: 2012

© Institute of Mathematics, NAS of Belarus