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

Samuel Albert; Bernardo Cockburn; Donald A. French; Todd E. Peterson

doi:10.1090/S0025-5718-01-01346-1

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

Samuel Albert, Bernardo Cockburn, Donald A. French, Todd E. Peterson

Mathematics

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16 Scopus citations

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.

Original language	English (US)
Pages (from-to)	49-76
Number of pages	28
Journal	Mathematics of Computation
Volume	71
Issue number	237
DOIs	https://doi.org/10.1090/S0025-5718-01-01346-1
State	Published - 2002

Keywords

Error estimates
Hamilton-Jacobi

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AU - Peterson, Todd E.

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AB - 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.

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JO - Mathematics of Computation

JF - Mathematics of Computation

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ER -

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

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