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Adaptive finite element methods for conservation laws based on a posteriori error estimates
Author(s) -
Johnson Claes,
Szepessy Anders
Publication year - 1995
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160480302
Subject(s) - mathematics , a priori and a posteriori , conservation law , finite element method , orthogonality , galerkin method , discontinuous galerkin method , entropy (arrow of time) , mathematical optimization , mathematical analysis , geometry , philosophy , physics , epistemology , quantum mechanics , thermodynamics
We prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite‐element method. The strong stability estimate uses the entropy condition for the system in an essential way. ©1995 John Wiley & Sons, Inc.