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We propose consistent locally stabilized, conforming finite element schemeson completely unstructured simplicial space-time meshes for the numericalsolution of non-autonomous parabolic evolution problems under the assumption ofmaximal parabolic regularity. We present new a priori estimates forlow-regularity solutions. In order to avoid reduced convergence rates appearingin the case of uniform mesh refinement, we also consider adaptive refinementprocedures based on residual a posteriori error indicators. The huge system ofspace-time finite element equations is then solved by means of GMRESpreconditioned by algebraic multigrid.

Space-Time Finite Element Methods for Parabolic Evolution Problems with Non-smooth Solutions