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On a cell entropy inequality for discontinuous Galerkin methods
Authors:
Guang Shan Jiang and Chi-Wang Shu
Journal:
Math. Comp. 62 (1994), 531-538
MSC:
Primary 65M60; Secondary 35L65, 65M12
MathSciNet review:
1223232
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: We prove a cell entropy inequality for a class of high-order discontinuous Galerkin finite element methods approximating conservation laws, which implies convergence for the one-dimensional scalar convex case.
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streamline diffusion finite element methods for hyperbolic conservation
laws, Math. Comp. 54
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(90j:65118), http://dx.doi.org/10.1090/S0025-5718-1990-0995210-0
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Tadmor, On the convergence of difference
approximations to scalar conservation laws, Math. Comp. 50 (1988), no. 181, 19–51. MR 917817
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H. Yang, Extremum tracking and convergence of semi-discrete TVD schemes, preprint.
- [1]
- R. Biswas, K. Devine, and J. Flaherty, Parallel, adaptive finite element methods for conservation laws, Appl. Numer. Math. (to appear). MR 1273828
- [2]
- F. Bouchut, C. Bourdarias, and B. Perthame, Un exemple de methode MUSCL satisfaisant toutes les inégalités d'entropie numériques, preprint.
- [3]
- B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework, Math. Comp. 52 (1989), 411-435. MR 983311 (90k:65160)
- [4]
- 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, Math. Comp. 54 (1990), 545-581. MR 1010597 (90k:65162)
- [5]
- B. Cockburn, F. Coquel, and P. Le Floch, An error estimate for finite volume methods for multidimensional conservation laws, Math. Comp. (to appear). MR 1240657 (95d:65078)
- [6]
- B. Cockburn and P. Gremaud, An error estimate for finite element methods for scalar conservation laws, preprint.
- [7]
- F. Coquel and P. Le Floch, Convergence of finite difference schemes for conservation laws in several space dimensions: the corrected antidiffusive flux approach, Math. Comp. 57 (1991), 169-210. MR 1079010 (91m:65229)
- [8]
- P. Lions and P. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C. R. Acad. Sci. Paris 311 (1990), 259-264. MR 1071622 (91i:65168)
- [9]
- C. Johnson, A. Szepessy, and P. Hansbo, On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws, Math. Comp. 54 (1990), 107-129. MR 995210 (90j:65118)
- [10]
- H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (1990), 408-463. MR 1047564 (91i:65157)
- [11]
- S. Osher, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal. 21 (1984), 217-235. MR 736327 (86d:65119)
- [12]
- -, Convergence of generalized MUSCL schemes, SIAM J. Numer. Anal. 22 (1985), 947-961. MR 799122 (87b:65147)
- [13]
- S. Osher and E. Tadmor, On the convergence of difference approximations to scalar conservation laws, Math. Comp. 50 (1988), 19-51. MR 917817 (89m:65086)
- [14]
- H. Yang, Extremum tracking and convergence of semi-discrete TVD schemes, preprint.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1994-1223232-7
PII:
S 0025-5718(1994)1223232-7
Keywords:
Conservation law,
discontinuous Galerkin,
entropy condition,
convergence
Article copyright:
© Copyright 1994 American Mathematical Society
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