A space-time finite element method for parabolic obstacle problems

Abstract: We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on simplicial and prismatic meshes are studied and we show a priori error estimates for both. Convergence rates are derived for sufficiently smooth solutions. Reliable a posteriori bounds are provided and used to steer an adaptive algorithm. Numerical experiments including a one-phase Stefan problem and an American option pricing problem are presented.