Métodos submalhas não lineares para o problema de convecção-difusão-reação

• Autor(a) principal: Santos, Isaac Pinheiro dos
• Data de Publicação: 2007
• 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/80
• topic: Método dos Elementos Finitos; Modelagem submalha; Viscosidade submalha não linear; Equação de convecção-difusão-reação; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

This work presents a general framework for approximating convection-diffusion-reaction equations based on principles of scale separation. A two-level decomposition of the discrete approximation spaces is performed and the local problem is modified introducing an artificial viscosity acting only on the subgrid scales. The key feature is the local control coming from the decomposition of the velocity field into the resolved and unresolved scales and requiring the satisfaction of the discrete model problem at the element level for a minimum kinetic energy associated to the unresolved scales. This procedure leads to a nonlinear subgrid model that acts only on the unresolved scales but does not require any tuned-up parameter. It can be considered a self adaptive method such that the amount of the subgrid viscosity is automatically introduced according to the residual of the resolved scale at element level. We provide an a priori error estimate with convergence rates similar to its linear counterpart and some other stabilized methods, like SUPG. Numerical experiments demonstrate the ability of the method to represent convection and/or reaction dominated problems.