University of Oulu

Lapin, A.V., Laitinen, E. The Regularized Mesh Scheme to Solve Quasilinear Parabolic Equation with Time-Fractional Derivative. Lobachevskii J Math 42, 1706–1714 (2021).

The regularized mesh scheme to solve quasilinear parabolic equation with time-fractional derivative

Saved in:
Author: Lapin, A. V.1; Laitinen, E.2
Organizations: 1Department of Higher Mathematics, Mechanics, and Mathematical Modelling, Institute of Personalized Medicine, Sechenov University, Moscow, 119435 Russia
2Faculty of Science, Research Unit of Mathematical Sciences, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.5 MB)
Persistent link:
Language: English
Published: Pleiades Publishing, 2021
Publish Date: 2022-03-14


A quasilinear parabolic problem with a time fractional derivative of the Caputo type and mixed boundary conditions is considered. The coefficients of the elliptic operator depend on the gradient of the solution, and this operator is uniformly monotone and Lipschitz-continuous. For this problem, unconditionally stable linear regularized semi-discrete scheme is constructed based on the L1-approximation of the fractional time derivative. Stability estimates are obtained by the variational method. Accuracy estimates are given provided that the initial data and the solution to the differential problem are sufficiently smooth. The proved result of stability of the semi-discrete scheme is valid for the mesh scheme obtained from the semi-discrete problem using the finite element method in spatial variables.

see all

Series: Lobachevskii journal of mathematics
ISSN: 1995-0802
ISSN-E: 1818-9962
ISSN-L: 1995-0802
Volume: 42
Issue: 7
Pages: 1706 - 1714
DOI: 10.1134/S1995080221070155
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Funding: This research was supported by Russian Foundation of Basic Researches, project no. 19-01-00431 and Academy of Finland, grant no. 333448 (Alexander Lapin) and Academy of Finland, grant no. 333551 (Erkki Laitinen).
Academy of Finland Grant Number: 333551
Detailed Information: 333551 (Academy of Finland Funding decision)
Copyright information: © The Author(s), 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit