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Adaptive Coupling and Fast Solution of FEM–BEM Equations for Parabolic–Elliptic Interface Problems
Author(s) -
Mund Patrick,
Stephan Ernst P.
Publication year - 1997
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/(sici)1099-1476(19970325)20:5<403::aid-mma816>3.0.co;2-5
Subject(s) - mathematics , finite element method , discretization , coupling (piping) , galerkin method , discontinuous galerkin method , boundary (topology) , a priori and a posteriori , parabolic partial differential equation , mathematical analysis , boundary value problem , interface (matter) , conjugate gradient method , method of mean weighted residuals , partial differential equation , mathematical optimization , physics , mechanics , mechanical engineering , bubble , maximum bubble pressure method , engineering , thermodynamics , philosophy , epistemology
In this paper we prove an a posteriori error estimate for the symmetric coupling of finite elements and boundary elements applied to linear parabolic–elliptic interface problems. The discontinuous Galerkin method is used for the discretization in time. We present an adaptive algorithm for choosing the mesh size in space and time and we analyse the Hybrid Modified Conjugate Residual (HMCR) method as a solution method for the linear systems which arise. Computational results show that the number of HMCR‐iterations grows slowly with the problem size. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.