Hybrid DG methods for Biot's consolidation problem

• Ano de defesa: 2018
• Autor(a) principal: Ledoino, Ismael de Souza
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Laboratório Nacional de Computação Científica; Coordenação de Pós-Graduação e Aperfeiçoamento (COPGA); Brasil; LNCC; Programa de Pós-Graduação em Modelagem Computacional
• Palavras-chave em Português: Elasticidade; Materiais porosos; Método de Galerkin descontínuo híbrido; CNPQ::CIENCIAS EXATAS E DA TERRA::GEOCIENCIAS::GEOLOGIA
• Link de acesso: https://tede.lncc.br/handle/tede/304

We propose a new mixed hybrid discontinuous Galerkin method for Biot’s consolidation problem. Our formulation is a mixed problem in three main unknowns: the displacement field, the pore pressure and a pseudo hydrostatic pressure, introduced with the purpose of obtaining a locking-free method. The hybridization consists of an introduction of Lagrange multipliers for the trace of the components of the displacement field and the pore pressure, to weakly impose the interface conditions on the edges of the elements. With this hybrid formulation, it is possible to obtain a global system involving only Lagrange multipliers degrees of freedom. Once the solution to the global system is obtained, one can calculate the solution to the primal variables by solving the local problems on element level. The numerical analysis is done using Babuška’s lemma, and numerical error estimates are provided in the energy norm, while estimates in the L2 norm are presented only for the associated linear elasticity problem. However, numerical experiments suggest that optimal convergence rates in the L2 norm are also obtained for Biot’s consolidation problem. As the analysis shows, numerical experiments verify that the method is stable even for equal order approximation for all variables, which generates more balanced convergence rates. Numerical experiments are also developed to provide clear evidence of the locking-free property.