Formulação de elementos finito mistas para problemas parabólicos lineares

• Autor(a) principal: Quinelato, Thiago de Oliveira
• Data de Publicação: 2013
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/173
• topic: Método dos elementos finitos; MÉTODO DOS ELEMENTOS FINITOS; Finite element method; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA::ANALISE NUMERICA

This work presents the main strategies for numerical solution of Darcy's and linear parabolic problems put into their mixed form. Approximations to second-order linear problems are traditionally obtained from finite element fomulations placed in a single field or based on compatible approximation spaces. Aiming an accurate computation of conservative and high-order fluxes we build a stabilized mixed-hybrid formulation for linear parabolic problems from the association of the implicit Euler method to a mixed-hybrid finite element method in its dual form. This formulation relies on stabilization strategies by the addition of least-squares residuals, already known for elliptic problems, which makes it possible to choose incompatible approximation spaces, while allowing to meet desired requirements of the physical problem, such as the continuity of the normal flow between elements. We use computer experiments and find that the method has the desired characteristics of mass conservation between elements and the possibility of obtaining higher-order approximations with respect to the spatial discretization.