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

Autor(es)

Devloo, Philippe R. B. ; Fernandes, Jeferson W. D. ; Gomes, Sonia M. ; Orlandini, Francisco T. ; Shauer, Nathan

• Tipo de documento: Artigo Científico
• Fonte: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING; v. 402, p. 28-pg., 2022-12-01.

Resumo

Exact finite element de Rham subcomplexes relate conforming subspaces in H1(12), H(curl; 12), H(div; 12), and L2(12) 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.(c) 2022 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 17/15736-3 - Centro de Pesquisa em Engenharia em Reservatórios e Gerenciamento de Produção de Petróleo
• Beneficiário: Denis José Schiozer
• Modalidade de apoio: Auxílio à Pesquisa - Programa Centros de Pesquisa em Engenharia
• Processo FAPESP: 21/03791-5 - Método multiescala e diagnóstico de escoamento para gerenciamento de reservatórios
• Beneficiário: Nathan Shauer
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 21/02187-7 - Explorar o uso de aproximação do método Multiscale Hybrid Mixed com pre-condicionador
• Beneficiário: Jeferson Wilian Dossa Fernandes
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado