Preprint 1997-010

Corrected operator splitting for nonlinear parabolic equations

Abstract: We present a corrected operator splitting (COS) technique for nonlinear parabolic equations of convection-diffusion type. The main feature of this method is the ability to correctly resolve steep fronts for large time steps, as opposed to standard operator splitting (OS) which fails do so. COS is based on solving a conservation law for modeling convection, a heat equation for modeling diffusion, and finally a certain ``residual'' conservation law for necessary correction. The residual equation, which is ignored in OS, has an anti-diffusive effect whose purpose is to counter-balance some of the diffusion introduced by the heat equation. It is shown that COS generates a compact sequence of approximate solutions which converges to the solution of the problem. The method of Dafermos constitutes an important part of our solution strategy. Finally, some numerical examples are presented.

Paper:

Available as PostScript

Title:

Author(s):

Kenneth Hvistendahl Karlsen, mailto:kennethk@mi.uib.no

Nils Henrik Risebro , mailto:nilshr@math.uio.no

Publishing information:

Report (applied mathematics) No. 108, University of Bergen, Bergen, Norway.

Comments:

Submitted by:

mailto:kennethk@mi.uib.no April 28 1997.