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Analysis of a mesh-dependent stabilization for the three fields domain decomposition method

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Abstract

We consider a stabilized version of the three fields domain decomposition method in the finite element framework, by a variant of the stabilization proposed in [2]. Under fairly general conditions on the meshes and on the finite element discretization considered we prove that for both the two dimensional and the three dimensional case the stabilized method retains the optimality/sub-optimality properties allowed by the interpolation in the underlying discretization spaces.

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Acknowledgments

I would like to thank the anonymous reviewers for their helpful comments and suggestions, and, in particular, for prompting me to include the case of the mortar multiplier. Work partially supported by Project MIUR-PRIN 2012 (2012HBLYE4) “Innovative methodologies for PDE based numerical modeling”.

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Authors and Affiliations

  1. CNR, IMATI “Enrico Magenes”, v. Ferrata 1, 27100, Pavia, Italy

    Silvia Bertoluzza

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  1. Silvia Bertoluzza
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Correspondence to Silvia Bertoluzza.

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Bertoluzza, S. Analysis of a mesh-dependent stabilization for the three fields domain decomposition method. Numer. Math. 133, 1–36 (2016). https://doi.org/10.1007/s00211-015-0742-5

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  • DOI: https://doi.org/10.1007/s00211-015-0742-5

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