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 and Todd E. Peterson

Journal:
Math. Comp. **71** (2002), 49-76

MSC (2000):
Primary 54C40, 14E20; Secondary 46E25, 20C20

DOI:
https://doi.org/10.1090/S0025-5718-01-01346-1

Published electronically:
October 4, 2001

MathSciNet review:
1862988

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Abstract | References | Similar Articles | Additional Information

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, , and any given approximation, . This upper bound is independent of the method used to compute the approximation ; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of . Numerical experiments investigating the sharpness of the a posteriori error estimate are given.

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Additional Information

**Samuel Albert**

Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455

Email:
albert@math.umn.edu

**Bernardo Cockburn**

Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street S.E., Minneapolis, Minnesota 55455

Email:
cockburn@math.umn.edu

**Donald A. French**

Affiliation:
Department of Mathematical Sciences, University of Cincinnati, PO Box 210025, Cincinnati, Ohio 45221

**Todd E. Peterson**

Affiliation:
Department of Mathematical Sciences, George Mason University, MS 3F2, Fairfax, Virginia 22030

Email:
tpeters1@gmu.edu

DOI:
https://doi.org/10.1090/S0025-5718-01-01346-1

Keywords:
Error estimates,
Hamilton-Jacobi

Received by editor(s):
April 10, 1997

Received by editor(s) in revised form:
April 17, 2000

Published electronically:
October 4, 2001

Additional Notes:
The second author was partially supported by the National Science Foundation (Grant DMS-9807491) and by the University of Minnesota Supercomputer Institute.

The third author was partially supported by the Taft Foundation through the University of Cincinnati.

Article copyright:
© Copyright 2001
American Mathematical Society