An operator splitting method for nonlinear convection-diffusion equations |
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| Authors: | Kenneth Hvistendahl Karlsen Nils Henrik Risebro |
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| Institution: | (1) Department of Mathematics, University of Bergen, N–5008 Bergen, Norway; e-mail: kennethk@mi.uib.no, NO;(2) Department of Mathematics, University of Oslo, N–0316 Oslo, Norway; e-mail: nilshr@math.uio.no, NO |
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| Abstract: | Summary. We present a semi-discrete method for constructing approximate solutions to the initial value problem for the -dimensional convection-diffusion equation . 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 , dimensional splitting is used to reduce the -dimensional convection problem to a series of one-dimensional problems. We show that the method produces a compact sequence
of approximate solutions which converges to the exact solution. Finally, a fully discrete method is analyzed, and demonstrated
in the case of one and two space dimensions.
ReceivedFebruary 1, 1996 / Revised version received June 24, 1996 |
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| Keywords: | Mathematics Subject Classification (1991):35L65 |
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