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Higher Order Mortar Finite Element Methods in 3D with Dual Lagrange Multiplier Bases

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Abstract

Mortar methods with dual Lagrange multiplier bases provide a flexible, efficient and optimal way to couple different discretization schemes or nonmatching triangulations. Here, we generalize the concept of dual Lagrange multiplier bases by relaxing the condition that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the Lagrange multiplier space have the same dimension. We provide a new theoretical framework within this relaxed setting, which opens a new and simpler way to construct dual Lagrange multiplier bases for higher order finite element spaces. As examples, we consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements. Numerical results illustrate the performance of our approach.

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Authors and Affiliations

  1. Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany

    B. P. Lamichhane & B. I. Wohlmuth

  2. Department of Mathematics, Utrecht University, The Netherlands

    R. P. Stevenson

Authors
  1. B. P. Lamichhane
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  2. R. P. Stevenson
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  3. B. I. Wohlmuth
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Correspondence to B. P. Lamichhane.

Additional information

This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12, the Netherlands Organization for Scientific Research and by the European Community's Human Potential Programme under contract HPRN-CT-2002-00286.

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Lamichhane, B., Stevenson, R. & Wohlmuth, B. Higher Order Mortar Finite Element Methods in 3D with Dual Lagrange Multiplier Bases. Numer. Math. 102, 93–121 (2005). https://doi.org/10.1007/s00211-005-0636-z

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  • DOI: https://doi.org/10.1007/s00211-005-0636-z

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