On the rate of convergence of a TVD scheme for solving the problem of decay of discontinuity (Q2760616)
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scientific article; zbMATH DE number 1682183
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rate of convergence of a TVD scheme for solving the problem of decay of discontinuity |
scientific article; zbMATH DE number 1682183 |
Statements
13 December 2001
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hyperbolic conservation law
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nonstationary shock wave
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system of quasi-linear equations
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difference schemes
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discontinuous solutions
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On the rate of convergence of a TVD scheme for solving the problem of decay of discontinuity (English)
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Several reasons are discussed by virtue of which the wrong view-point was widely spread during a long time according to which higher-order accuracy difference schemes preserve their higher-order accuracy for thorough computation of discontinuous solutions. First results of this type may be found in the papers of \textit{V. V. Ostapenko} [Comput. Math. Math. Phys. 37, No. 10, 1161-1172 (1997; Zbl 1122.76355)] and of \textit{J. Casper} and \textit{M. H. Carpenter} [SIAM J. Sci. Comput. 19, No. 3, 813-828 (1998; Zbl 0918.76045)].
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