mortar methods with curved interfaces

revised version: April 2004
Bernd Flemisch, Jens Markus Melenk, and Barbara Wohlmuth
(Please use for correspondence this email).

Submission date: 21. Jan. 2004
Pages: 23
published in: Applied numerical mathematics, 54 (2005) 3-4, p. 339-361 
DOI number (of the published article): 10.1016/j.apnum.2004.09.007
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Abstract:
We analyze a nonoverlapping domain decomposition technique with curvilinear boundaries.The weak coupling at the curved interfaces is carried out in terms of Lagrange multiplier spaces. We use the abstract framework of mortar and blending elements to obtain a priori results for this nonconforming discretization scheme. Introducing a mesh dependent jump on the curved interfaces based on piecewise linear approximations of the interfaces, the consistency error for the piecewise linear approximation can be decomposed into a consistency error for blending elements and a variational crime. Numerical results illustrate the performance of the method.