Local discontinuous Galerkin methods for partial differential equations with higher order derivatives (Q1610513)
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scientific article; zbMATH DE number 1784220
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Local discontinuous Galerkin methods for partial differential equations with higher order derivatives |
scientific article; zbMATH DE number 1784220 |
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Local discontinuous Galerkin methods for partial differential equations with higher order derivatives (English)
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20 August 2002
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Local discontinuous Galerkin methods for the numerical solution of hyperbolic conservation laws were established as accurate and robust alternatives to finite volume schemes by \textit{B. Cockburn} and \textit{C.W. Shu} [J. Comput Phys. 141, No. 2, 199-224 (1998; Zbl 0920.65059)]. In the present report these developments are reviewed and new methods of this kind are developed for partial differential equations of higher-order. \(L^2\)-stability is proven for general nonlinear problems. Numerical tests are included.
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discontinuous Galerkin method
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stability
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error estimate
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post-processing
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numerical examples
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hyperbolic conservation laws
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