Artículos de revistas
Three Dimensional Hierarchical Mixed Finite Element Approximations With Enhanced Primal Variable Accuracy
Registro en:
Computer Methods In Applied Mechanics And Engineering. Elsevier Science Sa, v. 306, p. 479 - 502, 2016.
0045-7825
1879-2138
WOS:000376485100021
10.1016/j.cma.2016.03.050
Autor
Castro
Douglas A.; Devloo
Philippe R. B.; Farias
Agnaldo M.; Gomes
Sonia M.; de Siqueira
Denise; Duran
Omar
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) There are different possibilities of choosing balanced pairs of approximation spaces for dual (flux) and primal (pressure) variables to be used in discrete versions of the mixed finite element method for elliptic problems arising in fluid simulations. Three cases shall be studied and compared for discretized three dimensional formulations based on tetrahedral, hexahedral and prismatic meshes. The principle guiding the constructions is the property that the divergence of the dual space and the primal approximation space should coincide, while keeping the same order of accuracy for the flux variable and varying the accuracy order of the primal variable. There is the classic case of BDMk spaces based on tetrahedral meshes and polynomials of total degree k for the dual variable, and k - 1 for the primal variable, showing stable simulations with optimal convergence rates of orders k + 1 and k, respectively. Another case is related to RTk and BDFMk+1 spaces for hexahedral and tetrahedral meshes, respectively, but holding for prismatic elements as well. It gives identical approximation order k + 1 for both primal and dual variables, an improvement in accuracy obtained by increasing the degree of primal functions to k, and by enriching the dual space with some properly chosen internal shape functions of degree k + 1, while keeping degree k for the border fluxes. A new type of approximation is proposed by further incrementing the order of some internal flux functions to k + 2, and matching primal functions to k + 1 (higher than the border fluxes of degree k). Thus, higher convergence rate of order k + 2 is obtained for the primal variable. Using static condensation, the global condensed system to be solved in all the cases has same dimension (and structure), which is proportional to the space dimension of the border fluxes for each element geometry. Illustrating results comparing the three different space configurations are presented for simulations based on hierarchical high order shape functions for H(div)-conforming spaces, which are specially constructed for affine tetrahedral, hexahedral and prismatic meshes. Expected convergence rates are obtained for the flux, pressure and divergence variables. (C) 2016 Elsevier B.V. All rights reserved. 306 479 502 ANP-Brazilian National Agency of Petroleum, Natural Gas and Biofuels [SAP4600333146] CNPq Brazilian Research Council [310369/2006-1, 308632/2006-0] FAPESP-Research Foundation of the State of Sao Paulo, Brazil [2013/21959-4] ANP [SAP4600333146] CAPES Foundation, within the Ministry of Education in Brazil (Grant PNPD/CAPES) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)