@article{Hou2023, 
author = {Yaxin Hou and Cao Wen and Yang Liu and Hong Li},
title = {A two-grid ADI finite element approximation for a nonlinear distributed-order fractional sub-diffusion equation},
year = {2023},
journal = {Networks and Heterogeneous Media},
volume = {18},
number = {2},
pages = {855-876},
keywords = {stability, WSGD operator, error estimates, nonlinear distributed-order fractional sub-diffusion equation, two-grid ADI FE method},
url = {https://www.sciopen.com/article/10.3934/nhm.2023037},
doi = {10.3934/nhm.2023037},
abstract = {In this paper, a two-grid alternating direction implicit (ADI) finite element (FE) method based on the weighted and shifted Grünwald difference (WSGD) operator is proposed for solving a two-dimensional nonlinear time distributed-order fractional sub-diffusion equation. The stability and optimal error estimates with second-order convergence rate in spatial direction are obtained. The storage space can be reduced and computing efficiency can be improved in this method. Two numerical examples are provided to verify the theoretical results.}
}