mortar methods with curved interfaces

Bernd Flemisch, Jens Markus Melenk, and Barbara Wohlmuth

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Submission date: 21. Jan. 2004 (revised version: April 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.