An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form (Q1091093)
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scientific article; zbMATH DE number 4009751
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form |
scientific article; zbMATH DE number 4009751 |
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An \(H^ 1\)-Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form (English)
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1987
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A one-dimensional single-phase Stefan problem is studied both from the theoretical and numerical view point. The problem is first transformed into a quasilinear parabolic equation which is not in divergence form. This parabolic problem is studied through a variational (weak) formulation. Approximation by an \(H^ 1\)-Galerkin procedure is then discussed and optimal error estimates in \(L^ 2\), \(H^ 1\), \(H^ 2\) norms are obtained.
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Galerkin method
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finite elements
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nondivergence form
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single-phase Stefan problem
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quasilinear parabolic equation
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optimal error estimates
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