A priori error estimates for approximate solutions to convex conservation laws |
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Authors: | Marc Küther |
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Institution: | (1) Institut für Angewandte Mathematik, Hermann-Herder Str. 10, 79104 Freiburg, Germany; e-mail: marc@mathematik.uni-freiburg.de , DE |
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Abstract: | Summary. We introduce a new technique for proving a priori error estimates between the entropy weak solution of a scalar conservation
law and a finite–difference approximation calculated with the scheme of Engquist-Osher, Lax-Friedrichs, or Godunov. This technique
is a discrete counterpart of the duality technique introduced by Tadmor SIAM J. Numer. Anal. 1991]. The error is related
to the consistency error of cell averages of the entropy weak solution. This consistency error can be estimated by exploiting
a regularity structure of the entropy weak solution. One ends up with optimal error estimates.
Received December 21, 2001 / Revised version received February 18, 2002 / Published online June 17, 2002 |
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Keywords: | Mathematics Subject Classification (1991): 65M15 76M12 35L65 |
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