2025/03/10 by J Carvajal, Davood Damircheli, Carvajal, José Joaquín +7
Computer Science · Engineering · #49J40 #58E35 #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2503.07808
openalex publication_date 2025/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.