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A posteriori error analysis for a boundary element method with nonconforming domain decomposition
Author(s) -
Domínguez Catalina,
Heuer Norbert
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21847
Subject(s) - mathematics , domain decomposition methods , estimator , mortar methods , discretization , norm (philosophy) , partial differential equation , a priori and a posteriori , discretization error , finite element method , polygon mesh , boundary value problem , error analysis , domain (mathematical analysis) , mathematical analysis , geometry , statistics , epistemology , political science , law , thermodynamics , philosophy , physics
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a nonconforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasireliability and efficiency of the error estimator in comparison with the error in a natural (nonconforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 947–963, 2014