Preprint 1996-002

An Operator Splitting Method for Convection-Diffusion Equations

Kenneth Hvistendahl Karlsen and Nils Henrik Risebro

Abstract: We present a semi-discrete method for constructing approximate solutions to the $m$-dimensional $(m\ge 1)$ convection-diffusion equation $u_{t}+\nabla\cdot \bF(u) =\eps\Delta u$. The method is based on the use of operator splitting to isolate the convection part and the diffusion part of the equation. In the case $m>1$, dimensional splitting is used to reduce the $m$-dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence of approximate solutions. Finally, a fully discrete method is analyzed, and demonstrated in the case of one and two space dimensions.

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An Operator Splitting Method for Convection-Diffusion Equations
Kenneth Hvistendahl Karlsen,
Nils Henrik Risebro,
Publishing information:
Report 101 1996, Dept. of Math., UiB. To appear in Numer. Math.
Submitted by: June 11 1996.

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