Finite-difference approximation of a one-dimensional Hamilton-Jacobi/elliptic system arising in superconductivity

被引：1

作者：

Briggs, AJ ^{[1
]}

Claisse, JR ^{[1
]}

Elliott, CM ^{[1
]}

机构：

[1] Univ Sussex, Ctr Math Anal & Its Applicat, Brighton BN1 9QH, E Sussex, England

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2002年 / 22卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Hamilton-Jacobi equation; elliptic-hyperbolic system; vortex density; evolution; superconductivity; finite difference schemes; viscosity solutions;

D O I：

10.1093/imanum/22.1.89

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Finite-difference approximations to an elliptic-hyperbolic system arising in vortex density models for type II superconductors are studied. The problem can be formulated as a non-local Hamilton-Jacobi equation on a bounded domain with zero Neumann boundary conditions. Monotone schemes are defined and shown to be stable. An L-infinity error bound is proved for the approximations of the unique viscosity solution.

引用

页码：89 / 131

页数：43

共 24 条

[1]

[Anonymous], 1997, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations

[2] FULLY NONLINEAR NEUMANN TYPE BOUNDARY-CONDITIONS FOR 1ST-ORDER HAMILTON-JACOBI EQUATIONS [J].

BARLES, G ;

LIONS, PL .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1991, 16 (02) :143-153

[3]

Barles G., 1994, Solutions de viscosite des equations de Hamilton-Jacobi, V17

[4] Computer modelling of type II superconductors in applications [J].

Barnes, G ;

McCulloch, M ;

Dew-Hughes, D .

SUPERCONDUCTOR SCIENCE & TECHNOLOGY, 1999, 12 (08) :518-522

[5]

BRIGGS AJ, 1999, 9909 U SUSS

[6]

Chapman S. J., 1996, EUR J APPL MATH, V7, P97, DOI 10.1017/S0956792500002242

[7] A MEAN-FIELD MODEL OF SUPERCONDUCTING VORTICES IN 3 DIMENSIONS [J].

CHAPMAN, SJ .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (05) :1259-1274

[8] A hierarchy of models for type-II superconductors [J].

Chapman, SJ .

SIAM REVIEW, 2000, 42 (04) :555-598

[9]

CLAISSE JR, 2000, THESIS SUSSEX U

[10]

CRANDALL MG, 1984, MATH COMPUT, V43, P1, DOI 10.1090/S0025-5718-1984-0744921-8

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