Weighted least-squares approximations to nonlinear hyperbolic equations (Q1770673)
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scientific article; zbMATH DE number 2153509
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Weighted least-squares approximations to nonlinear hyperbolic equations |
scientific article; zbMATH DE number 2153509 |
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Weighted least-squares approximations to nonlinear hyperbolic equations (English)
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7 April 2005
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The author considers a one-dimensional conservation law and a companion problem obtained by adding a small viscosity term. A numerical method based on time discretization and subsequent weighted least-squares finite element approximation is proposed and studied. The stability and the convergence of the method are shown in an appropriate norm. Methods for grid adaptation based on mesh redistribution are considered. Numerical results for the inviscid Burgers' equations are presented.
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finite elements
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mesh redistribution
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conservation law
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stability
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convergence
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numerical results
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Burgers' equations
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