2019 Apr 12, Alan Demlow, Texas A&M University Geometric errors in surface finite element methods

Alan Demlow, Texas A&M University
Geometric errors in surface finite element methods  
Surface finite element methods (SFEM) are widely used to approximately solve partial differential equations posed on surfaces. Such PDE arise in a range of applications, from image processing to fluid dynamics. Typical SFEM involve first approximating the underlying surface and then formulating the finite element method on the approximate surface. In this talk we discuss how approximation of the underlying surface affects the overall quality of the finite element approximation. The talk includes discussion of the effects of surface smoothness on geometric errors and some surprising recent results on approximation of surface eigenvalue problems.