Abstract: This talk is an introduction of the immersed finite element methods. We will start by recalling the standard finite element methods (FEM) for solving one-dimensional differential equations. Then we will introduce the immersed finite element (IFE) methods for differential equations with discontinuous coefficients (so-called interface problems). The advantage of IFE methods is that the mesh is independent of the interface, thus a uniform mesh can often be used. We will demonstrate how to construct IFE basis functions that can accommodate interface jump conditions. If time permits, we will talk about how to extend this immersed idea to two-dimensional interface problems.
This talk is accessible to graduate students and senior undergraduates in math major with some PDE and numerical analysis background.
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