Space-Time Continuous and Time Discontinuous Galerkin Schemes Based on Isogeometric Analysis for Nonlinear Time-Fractional Partial Differential Equations
Year: 2025
Author: Ang Ge, Jinye Shen, Lijun Yi
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 89–120
Abstract
This paper presents space-time continuous and time discontinuous Galerkin schemes for solving nonlinear time-fractional partial differential equations based on B-splines in time and non-uniform rational B-splines (NURBS) in space within the framework of Isogeometric Analysis. The first approach uses the space-time continuous Petrov-Galerkin technique for a class of nonlinear time-fractional Sobolev-type equations and the optimal error estimates are obtained through a concise equivalence analysis. The second approach employs a generalizable time discontinuous Galerkin scheme for the time-fractional Allen-Cahn equation. It first transforms the equation into a time integral equation and then uses the discontinuous Galerkin method in time and the NURBS discretization in space. The optimal error estimates are provided for the approach. The convergence analysis under time graded meshes is also carried out, taking into account the initial singularity of the solution for two models. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2308-m2023-0075
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 89–120
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 32
Keywords: Space-time Nonlinear time-fractional Sobolev-type equations Time-fractional Allen-Cahn equation Isogeometric analysis Error estimation.