References
- 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 viscosité 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 discontinuities.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.