Applied Mathematics Seminar

Speaker: Michael Neilan, Department of Mathematics, University of Pittsburgh

Title:  Finite Element Methods for Elliptic Problems in Non-divergence Form

Abstract: The finite element method is a powerful and ubiquitous tool in numerical analysis and scientific computing to compute  approximate solutions to partial differential equations (PDEs). A contributing factor of the method's success is that it naturally fits into the functional analysis framework of variational models. In this talk I will discuss finite element methods for PDEs problems that do not conform to the usual variational  framework, namely, elliptic PDEs in non--divergence form. I will first present the derivation of the scheme and  give a brief outline of the convergence analysis.  Finally,  I will present several challenging numerical examples showing the robustness of the method as well as verifying the theoretical results.