Investigation of Lagrange–Galerkin Method for an Obstacle Parabolic Problem
- Authors: Dautov R.Z.1, Lapin A.V.1,2
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Affiliations:
- Institute of Computational Mathematics and Information Technologies
- Coordinated Innovation Center for Computable Modeling in Management Science Tianjin University of Finance and Economics
- Issue: Vol 39, No 7 (2018)
- Pages: 884-892
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/202613
- DOI: https://doi.org/10.1134/S1995080218070089
- ID: 202613
Cite item
Abstract
The convergence and accuracy estimates are proved for Lagrange–Galerkin method, used for approximating the parabolic obstacle problem. The convergence analysis is based on the comparison of the solutions of Lagrange–Galerkin and backward Euler approximation schemes. First order in time step estimate for the difference of the solutions for above schemes in energy norm is proved under sufficiently weak requirements for the smoothness of the initial data. First order in time and space steps accuracy estimate for Lagrange–Galerkin method is derived in the case of discontinuous time derivative of the exact solution.
About the authors
R. Z. Dautov
Institute of Computational Mathematics and Information Technologies
Author for correspondence.
Email: rafail.dautov@gmail.com
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008
A. V. Lapin
Institute of Computational Mathematics and Information Technologies; Coordinated Innovation Center for Computable Modeling in Management Science Tianjin University of Finance and Economics
Email: rafail.dautov@gmail.com
Russian Federation, Kremlevskaya ul. 18, Kazan, Tatarstan, 420008; Tianjin, 300222