TY - JOUR
T1 - Space-Time Continuous and Time Discontinuous Galerkin Schemes Based on Isogeometric Analysis for Nonlinear Time-Fractional Partial Differential Equations
AU - Ge , Ang
AU - Shen , Jinye
AU - Yi , Lijun
JO - Journal of Computational Mathematics
VL - 1
SP - 89
EP - 120
PY - 2024
DA - 2024/11
SN - 43
DO - http://doi.org/10.4208/jcm.2308-m2023-0075
UR - https://global-sci.org/intro/article_detail/jcm/23531.html
KW - Space-time, Nonlinear time-fractional Sobolev-type equations, Time-fractional Allen-Cahn equation, Isogeometric analysis, Error estimation.
AB - <p style="text-align: justify;">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.</p>