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2007 | 17 | 3 | 403-412
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
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.
Rocznik
Tom
17
Numer
3
Strony
403-412
Opis fizyczny
Daty
wydano
2007
Twórcy
  • Institut de Mathématiques de Bordeaux and INRIA project Scalapplix, Université Bordeaux I, 341 Cours de la Libération, 33405 Talence, France
  • Department of Applied Mathematics, Université Bordeaux I, 341 Cours de la Libération, 33405 Talence, France
Bibliografia
  • 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.
  • 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.
  • Abgrall R. (2007): Construction of simple, stable and convergent high order schemes for steady first order Hamilton Jacobi equations. (in revision).
  • Abgrall R. and Perrier V. (2007): Error estimates for Hamilton-Jacobi equations with boundary conditions. (in preparation).
  • 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.
  • Bardi M. and Evans L.C. (1984): On Hopf's formula for solutions of first order Hamilton-Jacobi equations. Nonlinear Analysis Theory: Methods and Applications, Vol.8, No.11, pp.1373-1381.
  • Bardi M. and Osher S. (1991): The nonconvex multi-dimensional Riemann problem for Hamilton-Jacobi equations. SIAM Journal on Mathematical Analysis, Vol.22, No.2, pp.344-351.
  • Barles G. (1994): Solutions de viscosé des équations de Hamilton-Jacobi. Paris: Springer.
  • Barles G. and Souganidis P.E. (1991): Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis, Vol.4, No.3, pp.271-283.
  • Crandall M.G. and Lions P.L. (1984): Two approximations of solutions of Hamilton-Jacobi equations. Mathematics of Computation,Vol.43, No.167, pp.1-19.
  • Deckelnick K. and Elliot C.M. (2004): Uniqueness and error analysis for Hamilton-Jacobi equations with discontinuies. Interfaces and Boundary, Vol.6, No.3, pp.329-349.
  • Hu C. and Shu C.W. (1999): A discontinuous Galerkin finite element method for Hamilton Jacobi equations. SIAM Journal on Scientific Computing, Vol.21, No.2, pp.666-690.
  • 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.
  • Lions P.-L. (1982): Generalized Solutions of Hamilton-Jacobi Equations. Boston: Pitman.
  • 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.
  • 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.
  • 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
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-amcv17i3p403bwm
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