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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: 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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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

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