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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2024 Number 2, Pages 3–21 (Mi ivm9952)

Accuracy of an implicit scheme for the finite element method with a penalty for a nonlocal parabolic obstacle problem

O. V. Glazyrina, R. Z. Dautov, D. A. Gubaidullina

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia

Abstract: In order to solve a parabolic variational inequality with a nonlocal spatial operator and a one-sided constraint on the solution, a numerical method based on the penalty method, finite elements, and the implicit Euler scheme is proposed and studied. Optimal estimates for the accuracy of the approximate solution in the energy norm are obtained.

Keywords: finite element method, penalty method, parabolic variational inequality, implicit scheme, accuracy estimate.

UDC: 517.63

Received: 31.01.2023
Revised: 31.01.2023
Accepted: 29.03.2023

DOI: 10.26907/0021-3446-2024-2-3-21



© Steklov Math. Inst. of RAS, 2024