Friday, Sep 2, 2016 - 1:00pm - Allen 411
An introduction of 1D immersed finite element methods for differential equations with discontinuous coefficients
Dr. Xu Zhang, Mathematics, Msstate
Title: An introduction of 1D immersed finite element methods for differential equations with discontinuous coefficients
Abstract: This talk is an introduction of immersed finite element methods. we will first recall 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 coefficient jump, thus a uniform mesh can be used for such interface problems. We will demonstrate how to construct IFE basis functions that can accommodate interface jump conditions. We will also present the approximation capability, the error estimation, and the superconvergence behavior of IFE methods. If time permits, we will talk about how to extend this immersed idea to two-dimensional interface problems.
This talk is accessible to mathematician, graduate students and senior undergraduates in math major with some numerical analysis background.