An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions

Discontinuous Galerkin for Hamilton - Jacobi Equations

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

In this paper, we present a discontinuous Galerkin finite clement 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 ste...

A New Discontinuous Galerkin Method for Hamilton-Jacobi Equations

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, 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 nonconvex H...

A Central Discontinuous Galerkin Method for Hamilton-Jacobi Equations

In this paper, a central discontinuous Galerkin method is proposed to solve for the viscosity solutions of Hamilton-Jacobi equations. Central discontinuous Galerkin methods were originally introduced for hyperbolic conservation laws. They combine the central scheme and the discontinuous Galerkin method and therefore carry many features of both methods. Since Hamilton-Jacobi equations in general...

A Discontinuous Galerkin Moving Mesh Method for Hamilton-Jacobi Equations

where x = (x1, . . . , xd) ∈ IR , t > 0. HJ equations arise in many practical areas such as differential games, mathematical finance, image enhancement and front propagation. It is well known that solutions of (1) are Lipschitz continuous but derivatives can become discontinuous even if the initial data is smooth. There is a close relation between HJ equations and hyperbolic conservation laws. ...