Session B6 - Multiresolution and Adaptivity in Numerical PDEs - Semi-plenary talk
July 13, 15:30 ~ 16:20 - Room T1
Transport and Adaptivity
RWTH Aachen, Germany - firstname.lastname@example.org
Linear transport equations arise as limits of convection diffusion equations and form core constituents of kinetic models of Boltzmann type. We begin with indicating the importance of stable variational formulations of transport equations in such contexts. We discuss, in particular, the relevance of efficient and reliable a posteriori error bounds that have not been available so far. We then present some core ingredients of deriving such error bounds. We highlight essential distinctions from elliptic type problems which are mainly due to the anisotropic structure of the relevant function spaces arising in connection with transport problems. In particular, due to the fact that the a posteriori error indicators do not depend explicitly on mesh size parameters, it becomes much more involved to show that refinements, based on typical bulk-criteria, result in a fixed error reduction rate. We indicate some of the key ingredients and conclude with a short outlook on further consequences.
Joint work with Felix Gruber (RWTH Aachen), Olga Mula (Paris Dauphine University) and Rob Stevenson (University of Amsterdam).