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• W3043016770 abstract "In this work we present a generic framework for non-conforming finite elements on polytopal meshes, characterised by elements that can be generic polygons/polyhedra.Droniou, Jérôme We first present the functional framework on the example of a linear elliptic problem representing a single-phase flow in porous medium.Eymard, Robert This framework gathers a wide variety of possible non-conforming methods, and an error estimate is provided for this simple model.Gallouët, Thierry We then turn to the application of the functional framework to the case of a steady degenerate elliptic equation, for which a mass-lumping technique is required; here, this technique simply consists in using a different –piecewise constant– function reconstruction from the chosen degrees of freedom.Herbin, Raphaèle A convergence result is stated for this degenerate model. Then, we introduce a novel specific non-conforming method, dubbed Locally Enriched Polytopal Non-Conforming (LEPNC). These basis functions comprise functions dedicated to each face of the mesh (and associated with average values on these faces), together with functions spanning the local $$mathbb {P}^1$$ space in each polytopal element. The analysis of the interpolation properties of these basis functions is provided, and mass-lumping techniques are presented. Numerical tests are presented to assess the efficiency and the accuracy of this method on various examples. Finally, we show that generic polytopal non-conforming methods, including the LEPNC, can be plugged into the gradient discretization method framework, which makes them amenable to all the error estimates and convergence results that were established in this framework for a variety of models." @default.
• W3043016770 created "2020-07-23" @default.
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• W3043016770 date "2021-01-01" @default.
• W3043016770 modified "2023-09-24" @default.
• W3043016770 title "Non-conforming Finite Elements on Polytopal Meshes" @default.
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• W3043016770 doi "https://doi.org/10.1007/978-3-030-69363-3_1" @default.
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