Adaptive Galerkin methods with error control for a dynamical Ginzburg--Landau model in superconductivity (Q2706395)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Adaptive Galerkin methods with error control for a dynamical Ginzburg--Landau model in superconductivity |
scientific article |
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19 March 2001
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superconductivity
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error estimates
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error control
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time-dependent Ginzburg-Landau system
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magnetic field
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motion of vortices
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stability
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nonlinear parabolic equations
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Adaptive Galerkin methods with error control for a dynamical Ginzburg--Landau model in superconductivity (English)
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The paper deals with the time-dependent Ginzburg-Landau system. The authors deduce a posteriori estimates in order to find the necessary information for modifying the mesh and time-step according to the varying external magnetic field and the corresponding motion of vortices. The parabolic dual problem is also studied and the corresponding strong stability estimates are deduced. The methods developed in this paper can be extended to other classes of nonlinear parabolic equations with smooth nonlinearities.
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