Universität Augsburg
|
Herr Sai-Mang Pun
The Chinese University of Hong Kong
spricht am
Freitag, 14. Dezember 2018
um
12:00 Uhr
im
Raum 3008 (L1)
über das Thema:
Abstract: |
In this talk, we present the adaptive framework with the generalize multiscale finite element method (GMsFEM) in the mixed formulation. Firstly, we consider the goal-oriented adaptivity in the application to flow problem in heterogeneous media. Three different error indicators are considered: two, goal-oriented, and one a standard adaptive method for the global error. Each is used to approximate a number of quantities of interest given by interior edge fluxes in a high-contrast field. Following the setting of mixed GMsFEM, on each coarse neighborhood of the computational domain, the local error indicator introduced here is computed by the product of the residual norms of the primal and dual variational equations over coarse neighborhoods. In the second part, we consider the online adaptive enrichment within the framework of constraint energy minimizing GMsFEM. The online approach is based on the strategy of oversampling and makes use of the information of residual and the parameters in the partial differential equation such as the source function. The analysis presented shows that the error reduction can be made sufficiently large by suitably selecting oversampling regions and the number of oversampling layers. Numerical results are provided to illustrate the efficiency of the proposed methods. |
Hierzu ergeht herzliche Einladung. |
Prof. Dr. Daniel Peterseim |