EVENTO
Hybrid and Discontinuous FEM methods for porous media flow problems
Tipo de evento: Seminário de Avaliação - Série A
New Hybrid and Discontinuous FEM methods for porous media flow problems are proposed. Two classes of methods are devised: approximations (i) based on Least-Squares variational principles and (ii) combining classical Galerkin forms with Least-Squares residuals. Both primal and mixed discontinuous approximations are obtained following the same central ideas of the two approaches. The formulations are then hybridized, resulting in new hybrid discontinuous methods. Through this technique, low-order primal least-squares methods that were reported as impractical due to the regularity requirements and the associated computational cost as a consequence of the polynomial degrees in the element interior are now amended using static condensation. Primal Least-Squares formulations are related to classical primal hybrid methods, through symmetrization of the former, giving rise to adjoint consistent formulations. For mixed methods, a similar procedure is applied to obtain new formulations considering Least-Squares residuals. The hybridization follows the well-known HDG methods imposing local interface conditions (transmission conditions on the mesh skeleton). In all methods, the Lagrange multiplier is identified as the trace of the primal variable, resulting in a reduced number of unknowns when compared with the Least-Squares Weak Galerkin method, which uses two Lagrange multipliers, for instance. Considering a general scalar elliptic problem, we performed numerical experiments using the method of manufactured solutions to show that the new formulations have optimal convergence rates in terms of l2-norm for primal and flux (for mixed methods) variables. Additionally, the conditioning of resulting algebraic systems is assessed, showing similar results as in HDG even for nonsymmetric systems. To demonstrate the applicability of the new formulations, several porous media flow problems are solved: (i) Darcys flow in heterogeneous porous media, (ii) transport problem triggering instabilities, and (iii) double porosity/permeability Darcys flow problems.Para assistir acesse:meet.google.com/gbf-omuq-hpy
Data Início: 11/11/2022 Hora: 14:00 Data Fim: 11/11/2022 Hora: 17:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Virtual
Aluno: Diego Tavares Volpatto - -
Orientador: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC Antônio Tadeu Azevedo Gomes - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Eduardo Gomes Dutra do Carmo - Universidade Federal do Rio de Janeiro - UFRJ Maicon Ribeiro Correa - Universidade Estadual de Campinas - UNICAMP
Suplente Banca Examinadora: Regina Célia Cerqueira de Almeida - Laboratório Nacional de Computação Científica - LNCC
