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Approximation of H(div) with High-Order Optimal Finite Elements for Pyramids, Prisms and Hexahedra

Published online by Cambridge University Press:  03 June 2015

Morgane Bergot  and
Marc Duruflé
Morgane Bergot*
Affiliation:
CALVI project team, INRIA Nancy-Grand Est, Strasbourg, France
Marc Duruflé*
Affiliation:
BACCHUS project team, INRIA Bordeaux Sud-Ouest, Bordeaux, France
*
Corresponding author.Email:marc.durufle@inria.fr
Email:morgane.bergot@inria.fr
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Abstract

Classical facet elements do not provide an optimal rate of convergence of the numerical solution toward the solution of the exact problem in H(div-norm for general unstructured meshes containing hexahedra and prisms. We propose two new families of high-order elements for hexahedra, triangular prisms and pyramids that recover the optimal convergence. These elements have compatible restrictions with each other, such that they can be used directly on general hybrid meshes. Moreover the H(div) proposed spaces are completing the De Rham diagram with optimal elements previously constructed for H1 and H(curl) approximation. The obtained pyramidal elements are compared theoretically and numerically with other elements of the literature. Eventually, numerical results demonstrate the efficiency of the finite elements constructed.

Keywords

65M60Facet elementshigh-order finite elementpyramidsH(div) approximationDe Rham diagram

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 5 , November 2013 , pp. 1372 - 1414
Copyright
Copyright © Global Science Press Limited 2013

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