DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Michael Nielan, Pittsburgh

**Title: ***
Finite element methods for elliptic problems in non--divergence form
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**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.

**Time:** Friday, September 5, 2014, 1:30-2:30 p.m.

**Place:** Exploratory Hall (formerly S & T II), Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491