This framework proposes a method to improve error estimates in adaptive algorithms for parabolic obstacle problems, demonstrating its effectiveness through numerical experiments.
We propose and analyse a general framework for space-time finite element methods that is based on a first-order system least-squares 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.
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Carvajal et al. (2025) studied this question.
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