Session B6 - Multiresolution and Adaptivity in Numerical PDEs
July 14, 16:00 ~ 16:25
Aposteriori error analysis for $hp$-discontinuous Galerkin discretizations of parabolic problems
Free University of Bolzano-Bozen, Italy - firstname.lastname@example.org
We consider fully discrete space--time approximations of abstract linear parabolic partial differential equations (PDEs) consisting of an $hp$-version discontinuous Galerkin time stepping scheme in conjunction with standard (conforming) Galerkin discretizations in space. We derive computable aposteriori error bounds in the $\operatorname L_\infty(\operatorname L_2)$- and $\operatorname L_2(\operatorname H^1_0)$-type norms based on a novel space-time reconstruction approach.
Joint work with Emmanuil H Georgoulis (University of Leicester, GB, and National Technical University of Athens, GR) and Thomas P Wihler (Universität Bern, CH).