Speaker
Description
Instationary convection-diffusion problems arise in many applications, such as e.g., pollution simulations, heat transfer problems between thin domains, or in the modelling of flow and transport problems, to name but a few. In the advection-dominated case, the solutions are characterised by boundary layers, which lead to numerical instabilities and hence unphysical solutions when discretised with standard finite element methods. Known strategies to obtain stable solutions include the Streamline-Upwind Petrov-Galerkin (SUPG) method or a residual minimisation/least-squares approach. In this talk we focus on the latter approach. We will present an abstract least-squares framework that includes a built-in error estimator that can be used in a space-time adaptive refinement scheme. Furthermore, we will show that the instationary convection-diffusion equation fits into this framework and conclude with numerical examples that confirm our theoretical findings.
