EVENTO
Numerical Multiscale Methods
Tipo de evento: Seminário LNCC
We present some numerical multiscale methods. The methods are obtainedby taking enrichments of piecewise polynomials with special functions.We start by adding bubble functions to piecewise linears for the advective-diffusive model. We show that this Galerkin method is equivalent toSUPG with special stabilization parameter produced by the bubble shapefunctions. The method can be seen as an approximation to the fine scalesby the bubble functions. Their effect produces an improved numerical methodto the coarse scales. This is an example of numerical multiscale methods.Next we present a special class of bubble functions, the so-calledresidual-free bubble functions. They are obtained by enforcing thebubble part of the solution to satisfy strongly the pdes. We illustratethe method for the advective-diffusive equation.The solution at element-level of the residual-free bubble functions canbe complex. In these cases we approximate them by a two-level methodconsisting in solving the pdes by a suitable finite element methodat the element level. We illustrate this approach to the advectivediffusive method.The drawback of bubble functions is the enforcement of zero boundary conditions.This can be unacceptable to certain equations such as the reaction-diffusive equation when the reaction coefficient is much larger than the diffusive one.In these cases we use a Petrov-Galerkin enrichment method consisting inenriching the piecewise functions with functions that may not equal tozero in the boundary. We set the boundary conditions driven by residualsin the edges. The resulting method can be equally be seen as a multicaleapproach where the interior functions are approximations to the fine scalesthat improve the overall method for the coarse scales. The resulting methodis a stabilized-like method. We close the talk by applying these ideas to a simple finite element method for the Darcy model.
Data Início: 20/10/2008 Hora: 15:00 Data Fim: Hora: 16:30
Local: LNCC - Laboratório Nacional de Computação Ciêntifica - Auditorio A
Comitê Organizador: Leopoldo P. Franca - - -
Apoio Financeiro: CAPES
