High Order Numerical Discretization for Hamilton–Jacobi Equations on Triangular Meshes
Journal of Scientific Computing
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
Unconditionally stable methods for Hamilton--Jacobi equations
Journal of Computational Physics
Journal of Computational Physics
A Discontinuous Spectral Element Method for the Level Set Equation
Journal of Scientific Computing
A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Journal of Scientific Computing
Finite element level set formulations for modelling multiphase flows
ICCMSE '03 Proceedings of the international conference on Computational methods in sciences and engineering
High-order schemes for Hamilton-Jacobi equations on triangular meshes
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Hermite WENO schemes for Hamilton-Jacobi equations
Journal of Computational Physics
Journal of Computational Physics
Propagation of graphs in two-dimensional inhomogeneous media
Applied Numerical Mathematics - Numerical methods for viscosity solutions and applications
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
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
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
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
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
Journal of Scientific Computing
A local discontinuous Galerkin method for directly solving Hamilton-Jacobi equations
Journal of Computational Physics
Space-time discontinuous Galerkin finite element method for two-fluid flows
Journal of Computational Physics
Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities
SIAM Journal on Numerical Analysis
A boundary-only meshless method for numerical solution of the Eikonal equation
Computational Mechanics
A Discontinuous Galerkin Solver for Front Propagation
SIAM Journal on Scientific Computing
Uniformly Accurate Discontinuous Galerkin Fast Sweeping Methods for Eikonal Equations
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
The Chebyshev spectral viscosity method for the time dependent Eikonal equation
Mathematical and Computer Modelling: An International Journal
Optimal Trajectories of Curvature Constrained Motion in the Hamilton---Jacobi Formulation
Journal of Scientific Computing
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
An Adaptive Sparse Grid Semi-Lagrangian Scheme for First Order Hamilton-Jacobi Bellman Equations
Journal of Scientific Computing
Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes
Journal of Computational Physics
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
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In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton--Jacobi equations. This method is based on the Runge--Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high-order accuracy with a local, compact stencil, and is suited for efficient parallel implementation. One- and two-dimensional numerical examples are given to illustrate the capability of the method. At least kth order of accuracy is observed for smooth problems when kth degree polynomials are used, and derivative singularities are resolved well without oscillations, even without limiters.