The multiscale hybrid-mixed finite element method in polygonal meshes

Abstract : In this talk the recent extension of the Multiscale Hybrid-Mixed (MHM) method, originally proposed in [1], to the case of general polygonal meshes (that can be non-convex and non-conforming as well) will be presented. We present new stable multiscale finite elements such that they preserve the well-posedness, super-convergence and local conservation properties of the original MHM method under mild regularity conditions on the polygons. More precisely, we show that piecewise polynomial of degree k−1 and k, k≥1, for the Lagrange multipliers (flux) along with continuous piecewise polynomial interpolations of degree k posed on second-level sub-meshes are stable if the latter is refined enough. Such one- and two-level discretization impact the error in a way that the discrete primal (pressure) and dual (velocity) variables achieve super-convergence in the natural norms under extra local regularity only. Numerical tests illustrate theoretical results and the flexibility of the approach.
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https://hal.archives-ouvertes.fr/hal-02019259
Contributor : Fabrice Jaillet <>
Submitted on : Thursday, February 14, 2019 - 2:13:27 PM
Last modification on : Monday, August 19, 2019 - 9:54:12 AM

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  • HAL Id : hal-02019259, version 1

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Gabriel Raúl Barrenechea, Fabrice Jaillet, Diego Paredes, Frédéric Valentin. The multiscale hybrid-mixed finite element method in polygonal meshes. WONAPDE 2019, Jan 2019, Concepción, Chile. ⟨hal-02019259⟩

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