High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
Journal of Computational Physics
A level set approach for computing discontinuous solutions of Hamilton-Jacobi equations
Mathematics of Computation
A local piecewise parabolic method for Hamilton--Jacobi equations
Applied Numerical Mathematics
Journal of Computational Physics
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
A TVD-type method for 2D scalar Hamilton-Jacobi equations on unstructured meshes
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
Convex ENO Schemes for Hamilton-Jacobi Equations
Journal of Scientific Computing
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
Journal of Scientific Computing
A Second Order Central Scheme for Hamilton-Jacobi Equations on Triangular Grids
Numerical Analysis and Its Applications
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
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In this paper, we construct second-order central schemes for multidimensional Hamilton--Jacobi equations and we show that they are nonoscillatory in the sense of satisfying the maximum principle. Thus, these schemes provide the first examples of nonoscillatory second-order Godunov-type schemes based on global projection operators. Numerical experiments are performed; $L^1$/$L^{\infty}$-errors and convergence rates are calculated. For convex Hamiltonians, numerical evidence confirms that our central schemes converge with second-order rates, when measured in the L1-norm advocated in our recent paper [Numer. Math, to appear]. The standard $L^{\infty}$-norm, however, fails to detect this second-order rate.