Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity (Q2783766)
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scientific article; zbMATH DE number 1730740
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity |
scientific article; zbMATH DE number 1730740 |
Statements
Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity (English)
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17 April 2002
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elliptic-hyperbolic system
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vortex density models for type II superconductors
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finite-difference approximations
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non-local Hamilton-Jacobi equation
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monotone schemes
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viscosity solutions
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An elliptic-hyperbolic system arising in vortex density models for type II superconductors is studied by means of finite-difference approximations. The formulation of the problem involves a non-local Hamilton-Jacobi equation on a bounded domain subject to zero Neumann boundary conditions. Some monotone schemes are defined and shown to be stable, and an \(L^\infty\) error bound is established for the approximations of the unique viscosity solutions. Numerous graphical and numerical results are given.
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