Pré-Publication, Document De Travail Année : 2021

Exact sequences of conforming finite element spaces with interface constraints for general polytopal meshes

Résumé

In this work we give guidelines for the construction of new high order conforming finite element exact sequences of subspaces in H 1 (Ω), H(curl, Ω), H(div, Ω), and L 2 (Ω). They are meant for the design of stable conservative mixed formulations of multiphysics systems combined with advanced numerical strategies. For instance, they are defined to cope with general polytopal meshes and/or to allow trace interface constraints. These are appealing attributes for various challenging domains in computational practice, e.g. hp-adaptivity, meshing of complex regions, multiscale simulations etc. At each function space level, first we consider fixed trace spaces piece-wisely defined over given partitions of facets and/or edges of the mesh skeleton, and standard finite element exact sequences of composite polynomial approximations inside polytopal subdomains, based on conformal and regular partitions of them. Then, the construction of constrained subspaces only keeps the non-vanishing trace components constrained by the given (coarser) trace spaces, but the internal components of the original local finite element spaces, having vanishing traces, are all kept. These internal components may be richer in different extents when compared with the trace components: with respect to internal mesh size, internal polynomial degree, or both. In principle, the local polynomial degree, mesh resolution and geometry are allowed to vary over the different subdomains, but some compatibility properties are required on the meshes and polynomial spaces. Interpolants over the finite element subspaces verifying the commutative de Rham property are constructed in the spirit of projection-based operators, by the sum of linearly independent contributions associated with vertices, edges, faces, and volume, according to trace and internal components in each function level of the sequence.

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Dates et versions

hal-03189907 , version 1 (05-04-2021)

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  • HAL Id : hal-03189907 , version 1

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Philippe R B Devloo, Omar Duran, Sônia M Gomes. Exact sequences of conforming finite element spaces with interface constraints for general polytopal meshes. 2021. ⟨hal-03189907⟩
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