An Introduction to the Adaptive Finite Element Method

Start: 11/20/2013 - 4:15pm
End  : 11/20/2013 - 5:15pm


Ryan S. Szypowski, Cal Poly, Pomona


Abstract: The Finite Element Method is a common approach for approximating the solution to Partial Differential Equations. It has both an extremely rich theory as well as a simple and efficient algorithm. The algorithm is based on first producing a mesh of the domain and seeking a solution in a finite dimensional function space. In order to improve the accuracy, the mesh must be refined; however, for some problems, in order to maintain an optimal convergence rate, the mesh must be refined in certain areas more than other areas. This idea leads to the Adaptive Finite Element method which is based on computing an approximate solution, estimating the error in this solution, and deciding where to refine based on this estimate. In this talk, I will introduce the basic algorithm as well as show portions of the theory, including some recent results on the convergence of this procedure.

Davidson Lecture Hall, Claremont McKenna College

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