Análise teórica de uma técnica de aproximação da velocidade de Darcy utilizando o método dos elementos finitos mistos e híbridos

• Ano de defesa: 2009
• Autor(a) principal: Galdino, Paulo Henrique Barbosa
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Uberlândia; BR; Programa de Pós-graduação em Matemática; Ciências Exatas e da Terra; UFU
• Palavras-chave em Português: Elementos finitos; Métodos numéricos; Equações diferenciais parciais; Método dos elementos finitos; Finite elements; Numerical methods; Partial diferential equations; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufu.br/handle/123456789/16774

The objective of this work is to present one approach technique for the solution of elliptic equations, using Raviart-Thomas spaces of low order. Especially, the equation that supplies Darcy's velocities for flow in porous media it will be considered, taking into account both scalar permeability and permeability in the tensor form, defined in regular meshes of a rectangular domain. The technique used is known as mixed finite and hybrid elements method. In this case, the main variable of the linear system derived from the discretization is named Multiplier of Lagrange that is associated with each edges of the finite elements (hybrid formulation). In the mixed formulation, two appropriate spaces are considered: one contains scalar functions and the other contains vectorial functions. Thus, it can be approached, simultaneously, the pressure and the pressure gradient. The main result of this study is the demonstration, using local arguments, of the fact that the linear system associated to a weak formulation of the Darcy equations, with Lagrange Multipliers related to the normal flow that approach the pressure in the edges, has a matrix symmetric and positive definite.