EVENTO
Multiscale Hybrid-Mixed Finite Element Methods and Numerical Zoom
Tipo de evento: Seminário LNCC
This work proposes a new family of finite element methods for porous media flows, named Multiscale Hybrid-Mixed (MHM) methods. The MHM method is a consequence of a hybridization procedure, and emerges as a method that naturally incorporates multiple scales while provides solutions with high-order precision for the primal and dual (or flux) variables. The computation of local problems is embedded in the upscaling procedure, which are completely independent and thus may be naturally obtained using parallel computation facilities. Also interesting is that the flux variable preserves the local conservation property using a simple post-processing of the primal variable. The general framework is illustrated for the Darcy equation, and further extended to other operators taking part in the modeling of porous media flows (advection-diffusion and elasticity equations, for instance). The analysis results in a priori estimates showing optimal convergence in natural norms and providing a face-based a posteriori estimator. Regarding the latter, we prove that reliability and efficiency hold.Numerical results verify the optimal convergence properties as well as a capacity to accurately incorporate heterogeneity and high-contrast coefficients, showing in particular the great performance of the new a posteriori error estimator in driving mesh adaptativity. We conclude that the MHM method, along with its associated a posteriori estimator, is naturally shaped to be used in parallel computing environments and appears to be a highly competitive option to handle realistic multiscale boundary value problems with precision on coarse meshes.
Data Início: 01/10/2012 Hora: 14:00 Data Fim: Hora: 15:30
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Frédéric Gerard Christian Valentin - Laboratório Nacional de Computação Científica - LNCC - valentin@lncc.br
