OSU Mathematics Seminars and Colloquia
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Tue, Feb 11, 2020
Numerical Analysis Seminar
3:30 PM
MSCS 445
A General Framework For Immersed Finite Element Methods Based on A Cauchy Extension
Ruchi Guo, Ohio State University
Host: Xu Zhang
[Abstract] [PDF]
Abstract: Interface problems widely appear in many engineering applications which in general involve multiple materials coupled through interface and thus cause some challenges to numerical methods. Immersed finite element (IFE) methods are designed to solve interface problems on unfitted interface-independent meshes and the motivation is to remove the burden of mesh generation especially when the interface is moving. In this talk, I will describe a new general framework for the development and analysis of IFE methods based on the so called Cauchy extension which is applicable for any polynomial degree. In this framework, the IFE functions are constructed through solving local Cauchy problems locally on each interface element of which the boundary conditions are derived from the given jump conditions at the interface. Then many fundamental results including the existence, approximation capabilities and trace/inverse inequalities of IFE functions can be natural consequence of this local solver. Based on these results, we establish an optimal a-priori error estimate of IFE solutions in both the $L^2$ and $H^1$ norms.
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