A mollification based operator splitting method for convection diffusion equations

Authors:
Carlos D. Acosta;Carlos E. Mejía
Affiliations:
Universidad Nacional de Colombia, Department of Mathematics and Statistics, Manizales, Colombia;Universidad Nacional de Colombia, Department of Mathematics, Medellín, Colombia
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

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 Karlsen and Risebro (1997) [1] for a mollification step and prove that the convergence features are fairly well preserved. We end the paper with illustrative numerical experiments.