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A mollification based operator splitting method for convection diffusion equations. (English) Zbl 1189.65188

Summary: The main goal of this paper is to show that discrete mollification is a suitable ingredient in operator splitting methods for the numerical solution of nonlinear convection-diffusion equations. In order to achieve this goal, we substitute the second step of the operator splitting method of K. H. Karlsen and N. H. Risebro [Numer. Math. 77, No. 3, 365–382 (1997; Zbl 0882.35074)] for a mollification step and prove that the convergence features are fairly well preserved. We end the paper with illustrative numerical experiments.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K57 Reaction-diffusion equations

Citations:

Zbl 0882.35074
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References:

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