Mortar methods with curved interfaces

Authors:
B. Flemisch;J. M. Melenk;B. I. Wohlmuth
Affiliations:
Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany;MPI für Mathematik in den Naturwissenschaften, Inselstr. 22-26, D-04103 Leipzig, Germany;Institut für Angewandte Analysis und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
Venue:
Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
Year:
2005

Citing 3
Cited 2

Optimal finite-element interpolation on curved domains

SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods

Mixed and hybrid finite element methods
Multiplier Spaces for the Mortar Finite Element Method in Three Dimensions

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Mortar finite elements for interface problems

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An abstract framework for a priori estimates for contact problems in 3D with quadratic finite elements

Computational Mechanics

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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.