\(L1\)-multiscale Galerkin's scheme with multilevel augmentation algorithm for solving time fractional Burgers' equation
type: Item
instance of: scholarly article
title: \(L1\)-multiscale Galerkin's scheme with multilevel augmentation algorithm for solving time fractional Burgers' equation
zbMATH Open document ID: 1471.65136
DOI: 10.1155/2021/5581102
author: Jian Chen
author: Yong Huang
author: Taishan Zeng
published in: Journal of Function Spaces
publication date: 2021-05-04T00:00:00Z
review text: Summary: In this paper, we consider the initial boundary value problem of the time fractional Burgers equation. A fully discrete scheme is proposed for the time fractional nonlinear Burgers equation with time discretized by \(L1\)-type formula and space discretized by the multiscale Galerkin method. The optimal convergence orders reach \(\mathcal{O}(\tau^{2-\alpha} + h^r)\) in the \(L^2\) norm and \(\mathcal{O}(\tau^{2-\alpha} + h^{r-1})\) in the \(H^1\) norm, respectively, in which \(\tau\) is the time step size, \(h\) is the space step size, and \(r\) is the order of piecewise polynomial space. Then, a fast multilevel augmentation method (MAM) is developed for solving the nonlinear algebraic equations resulting from the fully discrete scheme at each time step. We show that the MAM preserves the optimal convergence orders, and the computational cost is greatly reduced. Numerical experiments are presented to verify the theoretical analysis, and comparisons between MAM and Newton's method show the efficiency of our algorithm.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7343375
zbMATH Keywords: time fractional Burgers' equation
zbMATH Keywords: Galerkin's scheme
zbMATH Keywords: multilevel augmentation method (MAM)
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5581102
OpenAlex ID: W3133680489
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description: scientific article; zbMATH DE number 7343375