A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations: part I: The steady state case

Authors:
Samuel Albert;Bernardo Cockburn;Donald A. French;Todd E. Peterson
Affiliations:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota;School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota;Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, Ohio;Department of Mathematical Sciences, George Mason University, MS 3F2, Fairfax, Virginia
Venue:
Mathematics of Computation
Year:
2002

Citing 6
Cited 6

The Neumann problem for nonlinear second order singular perturbation problems

SIAM Journal on Mathematical Analysis
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations

SIAM Journal on Numerical Analysis
Discrete time high-order schemes for viscosity solutions of Hamilton-Jacobi-Bellman equations

Numerische Mathematik
Numerical schemes for the Hamilton-Jacobi and level set equations on triangulated domains

Journal of Computational Physics
A Discontinuous Galerkin Finite Element Method for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Computational Differential Equations

Computational Differential Equations

A Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations

Journal of Scientific Computing
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions

Journal of Computational Physics
An adaptive method with rigorous error control for the Hamilton-Jacobi equations: part I: The one-dimensional steady state case

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part II: The two-dimensional steady-state case

Journal of Computational Physics
Essentially Non-Oscillatory Adaptive Tree Methods

Journal of Scientific Computing
An adaptive method with rigorous error control for the Hamilton--Jacobi equations. Part I: The one-dimensional steady state case

Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation

Quantified Score

Hi-index	0.01

Visualization

Abstract

A new upper bound is provided for the L∞-norm of the difference between the viscosity solution of a model steady state Hamilton-Jacobi equation, u, and any given approximation, v. This upper bound is independent of the method used to compute the approximation v; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of v. Numerical experiments investigating the sharpness of the a posteriori error estimate are given.