Maximum principle preserving schemes for interface problems with discontinuous coefficients (Q2780528)
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scientific article; zbMATH DE number 1729142
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Maximum principle preserving schemes for interface problems with discontinuous coefficients |
scientific article; zbMATH DE number 1729142 |
Statements
15 April 2002
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elliptic interface problem
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finite differences
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maximum principle
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discontinuous data
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convergence
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numerical examples
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Maximum principle preserving schemes for interface problems with discontinuous coefficients (English)
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The authors consider the elliptic problem NEWLINE\[NEWLINE (\beta u_x)_{x}+(\beta u_y)_{y}- \kappa(x,y)u=f(x,y) NEWLINE\]NEWLINE in a domain \(\Omega\) that contains a smooth curve \(\Gamma\) across which \(\beta\) and \(f\) may have jump discontinuities. The standard 5-point finite difference scheme is set up but modified near \(\Gamma\) in such a way that a discrete maximum principle is valid while the resulting scheme exhibits overall first order acuracy. Based on these properties convergence is proved. The authors study also a second order scheme starting from the 9-point finite difference stencil. The needed properties are in this case verified numerically. Numerical examples illustrate the theoretical results.
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