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Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations pp 401–433Cite as

Foundations of the MHM Method

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Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 114))

Abstract

An abstract setting for the construction and analysis of the Multiscale Hybrid-Mixed (MHM for short) method is proposed. We review some of the most recent developments from this standpoint, and establish relationships with the classical lowest-order Raviart-Thomas element and the primal hybrid method, as well as with some recent multiscale methods. We demonstrate the reach of the approach by revisiting the wellposedness and error analysis of the MHM method applied to the Laplace problem. In the process, we devise new theoretical results for this model.

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Author information

Authors and Affiliations

  1. Metropolitan State University of Denver, 173362, Campus Box 38, Denver, CO, 80217-3362, USA

    Christopher Harder

  2. National Laboratory for Scientific Computing - LNCC, Av. Getúlio Vargas, 333, 25651-070, Petrópolis, RJ, Brazil

    Frédéric Valentin

Authors
  1. Christopher Harder
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  2. Frédéric Valentin
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Correspondence to Frédéric Valentin .

Editor information

Editors and Affiliations

  1. Department of Mathematics & Statistics, University of Strathclyde, Glasgow, United Kingdom

    Gabriel R. Barrenechea

  2. Istituto di Matematica Applicata e Tecnologie Informatiche - Pavia, Consiglio Nazionale delle Ricerche, Pavia, Italy

    Franco Brezzi

  3. Department of Mathematics, University of Leicester, Leicester, United Kingdom

    Andrea Cangiani

  4. Department of Mathematics, National Technical University of Athens, Zografou, Greece

    Emmanuil H. Georgoulis

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Harder, C., Valentin, F. (2016). Foundations of the MHM Method. In: Barrenechea, G., Brezzi, F., Cangiani, A., Georgoulis, E. (eds) Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations. Lecture Notes in Computational Science and Engineering, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-41640-3_13

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