Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation (Q2814439)
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scientific article; zbMATH DE number 6596187
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation |
scientific article; zbMATH DE number 6596187 |
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Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation (English)
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22 June 2016
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Cahn-Hilliard-Hele-Shaw equation
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Darcy's law
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convex splitting
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finite difference method
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unconditional energy stability
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discrete Gagliardo-Nirenberg inequality
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discrete Gronwall inequality
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convergence
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error estimate
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The authors present an error analysis for an unconditionally energy stable, fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation, a modified Cahn-Hilliard equation coupled with the Darcy flow law. The approach relies on the convex splitting. First-order convergence (in time) and second-order convergence (in space) are derived. A discrete \(L^\infty_s(0,T; H^1_h)\cap L^2_h(0,T;H^3_h)\) error estimate is also obtained.
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