An enriched finite element space for boundary layer problems

Abstract: Abstract: The numerical solution of singularly perturbed PDEs is both interesting and challenging. In this talk, I'll first give a general introduction to these problems, and some of the numerous attempts to construct specialised numerical schemes that take into account the presence of any layers in the solutions. In the second part of the talk, I'll present a fitted operator-type approach, where we incorporate information on boundary layers into an otherwise standard finite element method. We'll also give some thought to the stability of the scheme, and the development of fast solvers.

This is joint work with Kirk Soodhalter and Adam Byrne (TCD).

Contact: Haixuan Yang

Mathematics

Audience: researchers in the discipline

Maths seminars at the University of Galway