On the numerical approximation of first-order Hamilton-Jacobi equations

• Autorzy: Abgrall R. , Perrier V.
• Języki publikacji: EN

Abstrakty

EN

Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.

Słowa kluczowe

EN

approximation of Hamilton-Jacobi equations; viscous solution; Cauchy-Dirichlet problem; triangular mesh

PL

równanie Hamiltona-Jacobiego; aproksymacja; zagadnienie Cauchy'ego-Dirichleta; siatka trójkątna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: Vol. 17, no 3
• Strony: 403--412
• Opis fizyczny: Bibliogr. 17 poz., rys.

Twórcy

autor

Abgrall R.

• Institut de Mathématiques de Bordeaux and INRIA project Scalapplix, Université Bordeaux I, 341 Cours de la Libération, 33 405 Talence

autor

Perrier V.

• Department of Applied Mathematics, Université Bordeaux I, 341 Cours de la Libération, 33 405 Talence Cedex, France

Bibliografia

• [1] Abgrall R. (1996): Numerical Discretization of First Order Hamilton-Jacobi Equations on Triangular Meshes. Communications on Pure and Applied Mathematics, Vol. XLIX, No. 12, pp. 1339-1373.
• [2] Abgrall R. (2004): Numerical discretization of boundary conditions for first order Hamilton Jacobi equations. SIAM Journal on Numerical Analyis, Vol. 41, No. 6, pp. 2233-2261.
• [3] Abgrall R. (2007): Construction of simple, stable and convergent high order schemes for steady first order Hamilton Jacobi equations. (in revision).
• [4] Abgrall R. and Perrier V. (2007): Error estimates for Hamilton-Jacobi equations with boundary conditions. (in preparation).
• [5] Augoula S. and Abgrall R. (2000): High order numerical discretization for Hamilton-Jacobi equations on triangular meshes. Journal of Scientific Computing, Vol. 15, No. 2, pp. 197-229.
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• [12] Hu C. and Shu C.W. (1999): A discontinuous Galerkin finite element method for Hamilton Jacobi equations. SIAMJournal on Scientific Computing, Vol. 21, No. 2, pp. 666-690.
• [13] Li F. and Shu C.W. (2005): Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations. Applied Mathematics Letters, Vol. 18, No. 11, pp. 1204-1209.
• [14] Lions P.-L. (1982): Generalized Solutions of Hamilton-Jacobi Equations. Boston: Pitman.
• [15] Osher S. and Shu C.W. (1991): High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations. SIAM Journal on Numerical Analysis, Vol. 28, No. 4, pp. 907-922.
• [16] Qiu J. and Shu C.W. (2005): Hermite WENO schemes for Hamilton-Jacobi equations. Journal of Computational Physics, Vol. 204, No. 1, pp. 82-99.
• [17] Zhang Y.T. and Shu C.W. (2003): High-order WENO schemes for Hamilton-Jacobi equations on triangular meshes. SIAM Journal on Scientific Computing, Vol. 24, No. 3, pp. 1005-1030.