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Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Approximation Theory of the P-finite Element Method

by
Professor Benqi Guo
Department of Mathematics, University of Manitoba, Canada

Date: April 14, 2004 (Wednesday)
Time: 4:30 pm to 5:30 pm
Venue: Room B6605 (Faculty Conference Room)
Blue Zone, Level 6
Academic Building
City University of Hong Kong

Abstract: In the framework of the Jacobi-weighted Besov and Sobolev spaces, the approximation of the P- finite element solutions in three dimensions is analyzed. For the optimal convergence for problems on polyhedral domains, Jacobi-weighted Besov and Sobolev spaces associated with three different Jacobi weights are introduced to precisely characterize the singularities and investigate the approximabilities of singular functions of three different types. These singularities occur in the solutions of problems with piecewise analytic data on polyhedral domains. Combining the approximabilities of singular and smooth parts of the solutions and the partition of unity technique, leads to the optimal convergence of the P-finite element solutions for problems on polyhedral domains.

Concluding remarks on effectiveness and robustness of this new mathematical framework for the one, two and three dimensions will be given. Also comments will be made on the applicability of this framework to the boundary element/spectral methods and prospect of a-posteriori error estimations of the P-finite element method.

(Tea, coffee and cookies will be provided at the Faculty Common Room in B6501 before the colloquium from 4:00 to 4:30 pm. Please come and join us!)

** All interested are welcome **

For enquiry: 2788-9816

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