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Towards a pollution-free finite element method for wave propagation

Tuesday, December 6, 3:30PM – 5PM
POB 6.304

Jay Gopalakrishan

"Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?", asked Babuska and Sauter in an influential early paper. Considering generalized FEM on 9-point stencils, they answered their (title) question in the negative. However, the situation is not hopeless for larger stencils, as we intend to convey. First, we present our suspicion that pollution-free methods exist, through numerical evidence collected from experiments with novel DPG schemes. Second, we present the design of a new scheme which under some assumptions yield pollution free theoretical error estimates. We conclude by connecting the first and the second steps. (This is ongoing joint work with Leszek Demkowicz and Ignacio Muga.)

Biosketch: Jay Gopalakrishnan is a numerical analyst and a computational scientist with interest in various technological applications. He taught at University of Florida for more than a decade. He just moved to Portland State University, where he now serves as a Professor of Mathematics and holds their Maseeh Distinguished Chair in Mathematical Sciences. His research interests center around the design of numerical methods for partial differential equations and their rapid solution by iterative techniques. In over forty publications, his work includes contributions to multigrid solvers and discontinuous Galerkin methods and other novel discretization techniques.

Hosted by Leszek Demkowicz