Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Weighted ENO Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
High-Resolution Nonoscillatory Central Schemes for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Numerical Discretization of Boundary Conditions for First Order Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Journal of Computational Physics
An Introduction to Eulerian Geometrical Optics (1992–2002)
Journal of Scientific Computing
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
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)
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
A second order discontinuous Galerkin fast sweeping method for Eikonal equations
Journal of Computational Physics
An Efficient Data Structure and Accurate Scheme to Solve Front Propagation Problems
Journal of Scientific Computing
On the Numerical Approximation of First-Order Hamilton-Jacobi Equations
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
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In this paper we construct several numerical approximations for first order Hamilton–Jacobi equations on triangular meshes. We show that, thanks to a filtering procedure, the high order versions are non-oscillatory in the sense of satisfying the maximum principle. The methods are based on the first order Lax–Friedrichs scheme [2] which is improved here adjusting the dissipation term. The resulting first order scheme is ϵ-monotonic (we explain the expression in the paper) and converges to the viscosity solution as {\cal O}(\sqrt{\Delta t}) for the L∞-norm. The first high order method is directly inspired by the ENO philosophy in the sense where we use the monotonic Lax–Friedrichs Hamiltonian to reconstruct our numerical solutions. The second high order method combines a spatial high order discretization with the classical high order Runge–Kutta algorithm for the time discretization. Numerical experiments are performed for general Hamiltonians and L1, L2 and L∞-errors with convergence rates calculated in one and two space dimensions show the k-th order rate when piecewise polynomial of degree k functions are used, measured in L1-norm.