Métodos mistos hibridizados descontínuos Galerkin para problemas de interface

• Autor(a) principal: Vargas Poblete, Héctor Andrés
• Data de Publicação: 2015
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/242
• topic: Análise numérica; Galerkin descontinuo; Métodos mixtos; Numerical analysis; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE

Both fitted and unfitted mixed hybrid discontinuous Galerkin (MHDG) finite element methods are proposed in this thesis to solve elliptic interface problems, providing high-order accuracy and computational efficiency. For the fitted case, the problems can be solved directly by the classical MHDG. For the unfitted case, we use broken base functions (unnecessary to satisfy the interface jump conditions) to those elements which are cut by interface. Unlike the immersed interface finite element methods (IIFEM), the two interface jumps are enforced weakly on the MHDG variational formulations. So, our unfitted MHDG can be applied more easily than IIFEM to general cases when the exact jump base function cannot be constructed. Numerical results on convergence and sensitivities of both interface location and different diffusion of the proposed methods are presented and discussed. Numerical analysis of the fitted MHDG method for diffusion interface problem is also given.