Mathematics Graduate Student Colloquium

An Interface-Fitted Mesh Generator and Virtual Element Methods for Elliptic Interface Problems

Min Wen
Wednesday, May 25, 2016
4:00 pm - 4:50 pm
RH440R

Talk Abstract:

We propose virtual element methods for solving one- or multi-domain elliptic interface problems using interface-fitted meshes. The main challenge is to design an efficient and robust mesh that can capture certain properties while preserving arbitrary complex geometries of the interface. Moreover, it is a tricky problem in classical finite element methods when the domain is decomposed into tetrahedra due to the existence of slivers in three dimensions. In our mesh generation, every element in three dimensions could be any polyhedron instead of tetrahedron. Then we apply virtual element methods for solving elliptic interface problems with solution and flux jump conditions. The purpose of using virtual element methods rather than classical finite element methods is that every element could be a different shape. We use multi-grid solvers to solve the discrete system. Lastly, numerical examples demonstrating the theoretical results for linear elements are shown.

About the Speaker:

Min is a 3rd year graduate student supervised by Prof. Long Chen. In her free time, she likes playing cards and scouting new restaurants on Yelp.

Advisor and Collaborators

Long Chen is Min's adviser.

Supplementary Materials:

none

Refreshments:

Pizza will be served after the talk.

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