EVENTO
Mixed Hybrid Finite Element Methods in Elasticity and Poroelasticity
Tipo de evento: Defesa de Tese de Doutorado
This thesis is focused on the development and analysis of finite dimensional approximations of the equations describing linear elasticity and poroelasticity problems. The approximation strategy is based on mixed hybrid finite element formulations of those problems and the construction of the finite dimensional spaces is guided by several desired properties: continuity of the tractions (conservation of linear momentum), symmetry of the stress tensor (conservation of angular momentum), reduced number of global degrees of freedom, and robustness on mesh distortion. The main difficulty is related with the simultaneous fulfillment of the inf-sup condition and the symmetry of the stress tensor. The last requirement is relaxed, being enforced in the weak sense through the introduction of a Lagrange multiplier. The greatest contribution is the development and analysis of stable finite dimensional spaces for mixed approximation of linear elasticity and poroelasticity problems on arbitrary quadrilateral meshes. These spaces are capable of providing optimal order convergence of the stress field in the H(div)-norm, both on meshes of squares and of arbitrary quadrilaterals, which is proved by numerical analysis and confirmed by experimentation.
Data Início: 13/03/2017 Hora: 10:00 Data Fim: 13/03/2017 Hora: 14:00
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Aluno: Thiago de Oliveira Quinelato - Universidade Federal de Juiz de Fora - UFJF
Co-Orientador: Maicon Ribeiro Correa - Universidade Estadual de Campinas - UNICAMP Todd James Arbogast - The University of Texas at Austin Department of Mathematics -
Orientador: Abimael Fernando Dourado Loula - Laboratório Nacional de Computação Científica - LNCC
Participante Banca Examinadora: Fernando A. Rochinha - PEM/COPPE - PEM/COPPE Frédéric Gerard Christian Valentin - Laboratório Nacional de Computação Científica - LNCC Álvaro Coutinho - COPPE/UFRJ - COPPE/UFRJ Todd James Arbogast - The University of Texas at Austin Department of Mathematics -
Suplente Banca Examinadora: Alexandre Loureiro Madureira - Laboratório Nacional de Computação Científica - LNCC Philippe Devloo - UNICAMP -
