High Order Immersed Finite Element Methods for Interface Problems


High Order Immersed Finite Element Methods for Interface Problems
Thursday, February 14, 2019
3:30PM – 5PM
POB 6.304

Slimane Adjerid

Many physical phenomena such as heat conduction and wave propagation in inhomogeneous media is modeled by partial differential equations with discontinuous coefficients referred to as interface problems. We introduce and motivate the immersed finite element approach for solving interface problems. The immersed finite element methods allow elements to be cut by the interface leading to special piecewise polynomial finite element spaces and modified weak formulations.

A brief historical review of immersed finite element methods will be presented. We will show how to construct high order immersed finite element spaces and weak Galerkin formulations for high accuracy computations. We will present computational results for several applications from acoustics and fluid dynamics and conclude with a list of open questions and future research projects.

Professor Adjerid received his PhD in mathematics from RPI in 1985. In 1998-2005 he was an Associate Professor of Mathematics and Virginia Tech. In 2005, he was Professor of Mathematics, Virginia Tech. His principal area of research is the dinite element methods for PDEs.

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