Adaptive Space-Time CFOSLS for Evolution Equations

Andreas Schafelner

Oct. 22, 2019, 3:30 p.m. S2 054

We present adaptive space-time finite element schemes based onconstrained first order system least squares (CFOSLS)formulations using the least squares functional restriced toindividual elements as indicators for adaptive refinements. Themarked elements are then refined using bisection. We considerboth parabolic and hyperbolic evolution problems, focusing onthe latter, in particular on the transport equation. Weperformed numerical experiments in parallel, and in both 3D and4D space-time, to illustrate the performance of the method.
This work is performed under the auspices of the U.S.Department of Energy by Lawrence Livermore National Laborartoryunder Contract DE-AC52-07NA27344.