Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations (Q932739)
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scientific article; zbMATH DE number 5300718
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations |
scientific article; zbMATH DE number 5300718 |
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Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations (English)
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11 July 2008
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The author proposes a new method for designing dissipative or conservative finite element schemes. The resulting schemes by the method can be implemented only with \(H^1\) elements. These schemes are suitable for Cahn-Hilliard, Korteweg-de Vries, and Schrödinger equations. The key device is the new concept of discrete partial derivatives. As application examples, three schemes for the Cahn-Hilliard, Korteweg-de Vries, and the nonlinear Schrödinger equations are presented. The effectiveness of this approach is illustrated on numerical examples.
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Galerkin method
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finite element method
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conservation
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dissipation
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nonlinear Schrödinger equation
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Cahn-Hilliard equation
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Korteweg-de Vries equation
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numerical example
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