Finite volume schemes for Hamilton-Jacobi equations

Numerische Mathematik

Volumn 83, Issue 3, 1999, Pages 427-442

  Kossioris, G ^a,c   Makridakis, Ch ^a,c   Souganidis, P E ^b,c  

^a UNIVERSITY OF CRETE   (Greece)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c INSTITUTE OF COMPUTER SCIENCE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033443186     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050457     Document Type: Article

References (13)

1. Abgrall, R. (1996): Numerical discretization of first order Hamilton-Jacobi equation on triangular meshes. Comm. Pure Appl. Math. 49, 1339-1373
2. Barles, G. (1994): Solutions de Viscosité des Équations de Hamilton-Jacobi. Mathématiques & Applications, vol. 17, Springer-Verlag, Paris
3. Barles, G., Souganidis, P.E. (1991): Convergence of approximation schemes for fully nonlinear second order equations. Asympt. Anal 4, 271-283
4. Brenner, S.C., Scott, L.R. (1994): The Mathematical Theory of Finite Element Methods. Springer-Verlag, New York
5. Chatzipantelidis, P. (1998): Finite volume and finite element methods for boundary and initial-boundary value problems. Ph. D. Thesis, Dept. of Math., University of Crete
6. Cockburn, B., Coquel, F., LeFloch, P. (1994): An error estimate for finite volume methods for conservation laws, Math. Comp. 64, 77-103
7. Crandall, M.G., Ishii, H., Lions, P.-L. (1992): User's guide to viscosity solutions of second order partial differential equations. Bul. AMS 27, 1-67
8. Crandall, M.G., Lions, P.-L. (1983): Viscosity solutions of Hamilton-Jacobi equations. Trans. Amer. Math. Soc. 277, 1-42
9. Crandall, M.G., Lions, P.-L. (1984): Two approximations of solutions of Hamilton-Jacobi equations. Math. Comp. 43, 1-19
10. Crouzeix, M., Raviart, P.A. (1973): Conforming and nonconforming finite element methods for solving the stationary Stokes equation I. RAIRO - Math. Mod. Num. Anal. 7, 77-104
11. Kossioris, G., Makridakis, Ch., Souganidis, P.E.: Finite volume methods for fully nonlinear problems, (in preparation)
12. Souganidis, P.E. (1985): Approximation schemes for viscosity solutions of Hamilton-Jacobi equations. J. Diff. Eqns 59, 1-43
13. Walkington, N. (1996): Algorithms for computing motion by mean curvature. SIAM J. Numer. Anal. 33, 2215-2238