A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions (Q977952)
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scientific article; zbMATH DE number 5725445
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions |
scientific article; zbMATH DE number 5725445 |
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A numerical analysis of the Cahn-Hilliard equation with dynamic boundary conditions (English)
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23 June 2010
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A finite element space semi-discretization of the Cahn-Hilliard equation with dynamic boundary conditions has been studied. Optimal error estimates in energy and weaker norms have been proved for sufficiently regular solutions. A convergence result in a weak sense for less regular solutions has also been proved. A fully discrete scheme based on the backward Euler scheme for the time discretization has been proposed and proved to be unconditionally stable. Some numerical examples are presented.
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finite element method
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error estimates
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backward Euler scheme
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linearized Crank-Nicolson scheme
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semilinear parabolic problem
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Łojasiewicz inequality
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semi-discretization
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Cahn-Hilliard equation
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convergence
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numerical examples
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