Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
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
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A Local Discontinuous Galerkin Method for KdV Type Equations
SIAM Journal on Numerical Analysis
High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes
SIAM Journal on Scientific Computing
A hybrid particle level set method for improved interface capturing
Journal of Computational Physics
Local discontinuous Galerkin methods for nonlinear dispersive equations
Journal of Computational Physics
Local discontinuous Galerkin methods for nonlinear Schrödinger equations
Journal of Computational Physics
A quadrature-free discontinuous Galerkin method for the level set equation
Journal of Computational Physics
A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect
Journal of Computational Physics
A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations
Journal of Scientific Computing
A uniformly second order fast sweeping method for eikonal equations
Journal of Computational Physics
Alternating evolution discontinuous Galerkin methods for Hamilton-Jacobi equations
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.46 |
In this paper we propose a new local discontinuous Galerkin method to directly solve Hamilton-Jacobi equations. The scheme is a natural extension of the monotone scheme. For the linear case with constant coefficients, the method is equivalent to the discontinuous Galerkin method for conservation laws. Thus, stability and error analysis are obtained under the framework of conservation laws. For both convex and noneconvex Hamiltonian, optimal (k+1)th order of accuracy for smooth solutions are obtained with piecewise kth order polynomial approximations. The scheme is numerically tested on a variety of one and two dimensional problems. The method works well to capture sharp corners (discontinuous derivatives) and have the solution converges to the viscosity solution.