Numerical Analysis and Scientific Computing Seminar | Volker John, On recent topics in the finite element analysis of convection-diffusion problems

For Zoom Link please contact ddelreyfernandez@uwaterloo.ca  

Speaker

Professor Volker John, Head of Research Group Numerical Mathematics and Scientific Computing Weierstrass Institute for Applied Analysis and Stochastics

Title

On recent topics in the finite element analysis of convection-diffusion problems 

Abstract

This talk considers finite element methods for scalar convection-diffusion problems and it discusses two recent topics of their analysis.

The first part of the talk is devoted to recent developments of the construction and numerical analysis of finite element methods for the steady-state problem that satisfy discrete maximum principles (DMPs). It turns out that many of the methods that satisfy DMPs and compute at the same time accurate solutions have been proposed only quite recently.

In the second part of the talk a proper orthogonal decomposition reduced order model (POD-ROM) method for the evolutionary problem is presented, which is augmented with a SUPG stabilization. An a priori error analysis which leads to robust estimates is discussed and an approach for posteriori error estimation is sketched. Numerical examples illustrate the performance of the SUPG-ROM method.