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An implicit–explicit residual error estimator for the coupling of dual‐mixed finite elements and boundary elements in elastostatics
Author(s) -
Gatica Gabriel N.,
Heuer Norbert,
Stephan Ernst P.
Publication year - 2001
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/1099-1476(200102)24:3<179::aid-mma204>3.0.co;2-m
Subject(s) - mathematics , sobolev space , finite element method , subspace topology , estimator , dirichlet distribution , norm (philosophy) , mathematical analysis , residual , a priori and a posteriori , boundary value problem , dirichlet boundary condition , neumann boundary condition , elasticity (physics) , algorithm , physics , philosophy , statistics , epistemology , political science , law , thermodynamics
We consider the coupling of dual‐mixed finite elements and boundary elements to solve a mixed Dirichlet–Neumann problem of plane elasticity. We derive an a‐posteriori error estimate that is based on the solution of local Dirichlet problems and on a residual term defined on the coupling interface. The general error estimate does not make use of any special finite element or boundary element spaces. Here the residual term is given in a negative order Sobolev norm. In practical applications, where a certain boundary element subspace is used, this norm can be estimated by weighted local L 2 ‐norms. Copyright © 2001 John Wiley & Sons, Ltd.