Preprint 1996002
An Operator Splitting Method for ConvectionDiffusion Equations
Kenneth Hvistendahl Karlsen and Nils Henrik Risebro
Abstract:
We present a semidiscrete method for constructing
approximate solutions to the $m$dimensional $(m\ge 1)$ convectiondiffusion
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 onedimensional 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.
 Paper:
 Available as PostScript
 Title:
 An Operator Splitting Method for ConvectionDiffusion Equations
 Author(s):

Kenneth Hvistendahl Karlsen,
<kennethk@mi.uib.no>
 Nils Henrik Risebro,
<nilshr@math.uio.no>
 Publishing information:
 Report 101 1996, Dept. of Math., UiB. To appear in Numer. Math.
 Submitted by:
 <kennethk@mi.uib.no>
June 11 1996.
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Last modified: Wed Jun 12 09:45:16 1996