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

Albert, Samuel; Cockburn, Bernardo; French, Donald; Peterson, Todd

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

Math. Comp. 71 (2002), 49-76 Request permission

Abstract:

A new upper bound is provided for the L$^\infty$-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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