Event Type:

Department Colloquium

Date/Time:

Tuesday, November 22, 2005 - 07:00

Location:

Kidd 364

Local Speaker:

Abstract:

Consider (1) F(U)=0 representing a system of partial differential equations solved for U, and its numerical counterpart (2) F_h(U_h)=0, solved for U_h, In this context, the keyword "adaptivity" refers to changing the spatial and temporal discretization in (2) so that the error of numerical approximation U-U_h is minimized while keeping the computational cost small. This is achieved via rigorous theory of a-posteriori error estimation which has which has been actively developed for finite element methods in the last 15 years. On the other hand, one

frequently is forced to use, instead of (1), its modification (3)

\tilde{F}( \tilde{U})=0; two important examples in porous media arise

in multiscale models and in coupled processes. However, it is

generally difficult to assess the modeling error U- \tilde{U} other

than by using costly sensitivity studies of U_h-\tilde{U}_h.

In the talk we present our past and recent results on, in particular,

i) the analysis of U- \tilde{U} for multiscale models of flow and

transport in porous media, and ii) a-posteriori estimates for U-U_h

for mixed mortar methods for flow. In addition, iii) we propose how to

adaptively and inexpensively define (3) so that the combined numerical

and modeling errors U-\tilde{U}_h can be assessed and controlled.