EVENTO
Hybrid DG Methods for Biots Consolidation Problem
Tipo de evento: Defesa de Dissertação de Mestrado
We propose a new Mixed Hybrid DG formulation for the Poroelasticity problem, written in terms of the porous medium displacement field, the pore pressure and a hidrostatic pressure, being the last essential for obtaining a locking-free formulation in the nearly incompressible regime. Using the Nitsche method, we introduce Lagrange multipliers identified with the trace of the displacement field and the trace of the pore pressure across the edges of the finite element mesh. The formulation obtained is stable even for equal order spaces, in constrast with continuous Galerkin (CG) formulations that require Taylor-Hood elements to achieve stability, since the displacement and pore pressure satisfy a Stokes problem in t=0. Because the pore pressure belongs to H1 for t>0, the flexibility on the choice of order spaces makes the global error of the hybrid formulation more equilibrated than the global error obtained from CG formulation. Furthermore, despite the fact that the proposed formulation has three variable fields, the overall computational cost is the one of a formulation written in terms only of the displacement and pore pressure, since one can eliminate the internal-element unknowns in terms of the Lagrange multiplier unknowns. We present the numerical analysis of the method using Babuskas Lemma to prove existence and uniqueness, and derive convergence rates in the Energy norm and L2 norm. Finally we comprove the locking-free property and the numerical estimates in several numerical experiments.
Data Início: 24/04/2018 Hora: 10:00 Data Fim: 24/04/2018 Hora: 13:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Aluno: Ismael de Souza Ledoino - Laboratório Nacional de Computação Científica - LNCC
Orientador: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Eduardo Gomes Dutra do Carmo - Universidade Federal do Rio de Janeiro - UFRJ José Karam Filho - Laboratório Nacional de Computação Científica - LNCC Yuri Higor Aguiar da Igreja - Universidade Federal de Juiz de Fora - UFJF
Suplente Banca Examinadora: Regina Célia Cerqueira de Almeida - Laboratório Nacional de Computação Científica - LNCC
