Construction of Locally Supported Biorthogonal Bases for Mortar Finite Element Discretizations and Applications
Bishnu P. Lamichhane (CMA, ANU)
MSI Computational Mathematics Seminar SeriesDATE: 2008-06-02
TIME: 11:00:00 - 12:00:00
LOCATION: John Dedman G35
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ABSTRACT:
The coupling of different discretization schemes or of nonmatching triangulations can be analyzed within the framework of mortar methods. These nonconforming domain decomposition techniques provide a more flexible approach than standard conforming approaches. They are of special interest for time-dependent problems, diffusion coefficients with jumps, problems with local anisotropies, sliding or moving subdomains, and when different physical models are used in different regions of the simulation domain. To obtain a stable and optimal discretization scheme for the global problem, the information transfer between the subdomains is of crucial importance.
We formulate an abstract framework for the mortar finite elements for optimal a priori estimate, and prove an improved error estimate in three dimensional mortar finite elements. We consider bases biorthogonal to the finite element space of arbitrary order in one dimension with optimal approximation properties, where the support of biorthogonal basis functions and finite element basis functions is the same. Working with Gauss-Lobatto nodes, optimal polynomial reproduction is obtained leading to an interesting connection between biorthogonality and quadrature formulas. We extend the ideas to three dimensional mortar finite elements for quadratic and serendipity finite elements.
Finally, we show some applications of mortar finite elements.
BIO:
http://wwwmaths.anu.edu.au/~lamichh/
