Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations

DOI10.1016/S0168-9274(99)00109-9zbMath0968.65073OpenAlexW2061569988MaRDI QIDQ1973820

Changqing Hu, Chi-Wang Shu, Olga Lepsky

Publication date: 1 May 2001

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(99)00109-9

zbMATH Keywords

complexityviscosity solutionnumerical examplesRunge-Kutta methoddiscontinuous Galerkin finite element methodweakly hyperbolic system

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Complexity and performance of numerical algorithms (65Y20)

Related Items (33)

Conservative high-order discontinuous Galerkin remap scheme on curvilinear polyhedral meshes ⋮ Finite volume Hermite WENO schemes for solving the Hamilton-Jacobi equations. II: Unstructured meshes ⋮ An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions ⋮ A sixth-order weighted essentially non-oscillatory schemes based on exponential polynomials for Hamilton-Jacobi equations ⋮ A new finite difference mapped unequal-sized WENO scheme for Hamilton-Jacobi equations ⋮ Hermite WENO schemes for Hamilton-Jacobi equations on unstructured meshes ⋮ WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations ⋮ A kernel based high order ``explicit unconditionally stable scheme for time dependent Hamilton-Jacobi equations ⋮ A discontinuous Galerkin finite element method for directly solving the Hamilton-Jacobi equations ⋮ Dimension-by-dimension moment-based central Hermite WENO schemes for directly solving Hamilton-Jacobi equations ⋮ A central discontinuous Galerkin method for Hamilton-Jacobi equations ⋮ An alternative formulation of discontinous Galerkin schemes for solving Hamilton-Jacobi equations ⋮ Error analysis of the high order scheme for homogenization of Hamilton-Jacobi equation ⋮ An arbitrary Lagrangian-Eulerian local discontinuous Galerkin method for Hamilton-Jacobi equations ⋮ Runge-Kutta discontinuous Galerkin methods for the special relativistic magnetohydrodynamics ⋮ A kernel-based explicit unconditionally stable scheme for Hamilton-Jacobi equations on nonuniform meshes ⋮ A finite differences method for a two-dimensional nonlinear hyperbolic equation in a class of discontinuous functions ⋮ Hamilton–Jacobi–Bellman Equations ⋮ Mapped WENO schemes based on a new smoothness indicator for Hamilton-Jacobi equations ⋮ High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton-Jacobi equations ⋮ A generalized approach for sub- and super-critical flows using the local discontinuous Galerkin method ⋮ A high-order discontinuous Galerkin method for level set problems on polygonal meshes ⋮ A high-order conservative remap for discontinuous Galerkin schemes on curvilinear polygonal meshes ⋮ Discontinuous Galerkin finite element in time for solving periodic differential equations ⋮ Optimal order error estimates for discontinuous Galerkin methods for the wave equation ⋮ On a family of discontinuous Galerkin fully-discrete schemes for the wave equation ⋮ Runge-Kutta Central Discontinuous Galerkin Methods for the Special Relativistic Hydrodynamics ⋮ Discontinuous Galerkin Methods for Solving Two Membranes Problem ⋮ A New Type of High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes ⋮ A GPU accelerated level set reinitialization for an adaptive discontinuous Galerkin method ⋮ Hermite WENO schemes for Hamilton-Jacobi equations ⋮ Unconditional stability and optimal error estimates of discontinuous Galerkin methods for the second-order wave equation ⋮ Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations

This page was built for publication: Analysis of the discontinuous Galerkin method for Hamilton-Jacobi equations