An efficient construction of divergence-free spaces in the context of exact finite element de Rham sequences

Exact finite element de Rham subcomplexes relate conforming subspaces in H1(Ω), H(curl;Ω), H(div;Ω), and L2(Ω) in a simple way by means of differential operators (gradient, curl, and divergence). The characteristics of such strong couplings are crucial for the design of stable and conservative discr...

Full description

Saved in:
Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2022-12, Vol.402, p.115476, Article 115476
Main Authors: Devloo, Philippe R.B., Fernandes, Jeferson W.D., Gomes, Sônia M., Orlandini, Francisco T., Shauer, Nathan
Format: Article
Language:English
Subjects:
Couplings
Differential equations
Divergence
Finite element exact sequences
Fluid flow
Incompressible flow
Mixed methods
Operators (mathematics)
Porous media
Robustness (mathematics)
Sequences
Shape functions
Strong divergence-free flux approximations
Subspaces
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Exact finite element de Rham subcomplexes relate conforming subspaces in H1(Ω), H(curl;Ω), H(div;Ω), and L2(Ω) in a simple way by means of differential operators (gradient, curl, and divergence). The characteristics of such strong couplings are crucial for the design of stable and conservative discretizations of mixed formulations for a variety of multiphysics systems. This work explores these aspects for the construction of divergence-free vector shape functions in a robust fashion allowing stable and faster simulations of mixed formulations of incompressible porous media flows. The resulting schemes are verified by means of numerical tests with known smooth solutions and applied to a benchmark problem to confirm the expected theoretical and computational performance results.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2022.115476