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Babuska Forum Series: Generalized Finite Element Method

Friday, April 29, 11AM – 12PM
POB 6.304

Uday Banerjee, Syracuse University

The talk will start with an intuitive description of the Finite Element Method (FEM). We will then introduce the idea of the Generalized Finite Element Method (GFEM) in the context of approximating non-smooth solutions of differential equations. We will highlight a potential problem, related to the solution of a linear system, in GFEM and show how the problem could be resolved by an easy modification of GFEM - the modified method is called the Stable Generalized Finite Element Method (SGFEM). FEM, GFEM, SGFEM involves solving linear systems. We will discuss the accuracy of numerical solutions of these linear systems (obtained by implementing algorithms in different computers), where we will indicate the need of "Validation" of a hypothesis related to the accuracy. This talk will be accessible to first year graduate students; only familiarity with basic mathematics (e.g., calculus/simple differential equations) and linear systems will be assumed.

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