Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations

Applied Mathematics Letters

Volumn 18, Issue 11, 2005, Pages 1204-1209

  Li, Fengyan ^a   Shu, Chi Wang ^a  

^a BROWN UNIVERSITY   (United States)

Author keywords

Discontinuous Galerkin method; Hamilton Jacobi equations

Indexed keywords

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

CURL-FREE PROPERTY; DISCONTINUOUS GALERKIN METHOD; HAMILTON-JACOBI EQUATIONS; STABILITY ANALYSIS;

GALERKIN METHODS;

EID: 25144454444     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2004.10.009     Document Type: Article

References (18)

1. R. Abgrall On essentially non-oscillatory schemes on unstructured meshes: Analysis and implementation Journal of Computational Physics 114 1994 45 58
2. B. Cockburn, S. Hou, and C.-W. Shu The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: the multidimensional case Mathematics of Computation 54 1990 545 581
3. B. Cockburn, F. Li, and C.-W. Shu Locally divergence-free discontinuous Galerkin methods for the Maxwell equations Journal of Computational Physics 194 2004 588 610
4. B. Cockburn, and C.-W. Shu The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems Journal of Computational Physics 141 1998 199 224
5. B. Cockburn, and C.-W. Shu Runge-Kutta discontinuous Galerkin methods for convection-dominated problems Journal of Scientific Computing 16 2001 173 261
6. M. Crandall, and P.L. Lions Viscosity solutions of Hamilton-Jacobi equations Transactions of the American Mathematical Society 277 1983 1 42
7. M. Crandall, and P.L. Lions Two approximations of solutions of Hamilton-Jacobi equations Mathematics of Computation 43 1984 1 19
8. S. Gottlieb, C.-W. Shu, and E. Tadmor Strong stability-preserving high-order time discretization methods SIAM Review 43 2001 89 112
9. C. Hu, and C.-W. Shu A discontinuous Galerkin finite element method for Hamilton-Jacobi equations SIAM Journal on Scientific Computing 21 1999 666 690
10. G. Jiang, and D. Peng Weighted ENO schemes for Hamilton-Jacobi equations SIAM Journal on Scientific Computing 21 1999 2126 2143
11. S. Jin, and Z. Xin Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, and relaxation schemes SIAM Journal on Numerical Analysis 35 1998 2385 2404
12. O. Lepsky, C. Hu, and C.-W. Shu Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations Applied Numerical Mathematics 33 2000 423 434
13. F. Li, C.-W. Shu, Locally divergence-free discontinuous Galerkin methods for MHD equations, Journal of Scientific Computing (in press)
14. P.L. Lions Generalized Solutions of Hamilton-Jacobi Equations 1982 Pitman Boston
15. S. Osher, and J. Sethian Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations Journal of Computational Physics 79 1988 12 49
16. S. Osher, and C.-W. Shu High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations SIAM Journal on Numerical Analysis 28 1991 907 922
17. C.-W. Shu, and S. Osher Efficient implementation of essentially non-oscillatory shock-capturing schemes Journal of Computational Physics 77 1988 439 471
18. Y.-T. Zhang, and C.-W. Shu High order WENO schemes for Hamilton-Jacobi equations on triangular meshes SIAM Journal on Scientific Computing 24 2003 1005 1030