Name
Title | ||
|---|---|---|
Error Estimates Of A Continuous Galerkin Time Stepping Method For Subdiffusion Problem |
Abstract | ||
|---|---|---|
A continuous Galerkin time stepping method is introduced and analyzed for subdiffusion problem in an abstract setting. The approximate solution will be sought as a continuous piecewise linear function in time t and the test space is based on the discontinuous piecewise constant functions. We prove that the proposed time stepping method has the convergence order O(tau(1+alpha)), alpha is an element of (0, 1) for general sectorial elliptic operators for nonsmooth data by using the Laplace transform method, where tau is the time step size. This convergence order is higher than the convergence orders of the popular convolution quadrature methods (e.g., Lubich's convolution methods) and L-type methods (e.g., L1 method), which have only O(tau) convergence for the nonsmooth data. Numerical examples are given to verify the robustness of the time discretization schemes with respect to data regularity. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s10915-021-01587-9 | JOURNAL OF SCIENTIFIC COMPUTING |
Keywords | DocType | Volume |
Subdiffusion problem, Continuous Galerkin time stepping method, Laplace transform, Caputo fractional derivative | Journal | 88 |
Issue | ISSN | Citations |
3 | 0885-7474 | 0 |
PageRank | References | Authors |
0.34 | 0 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuyuan Yan | 1 | 0 | 0.34 |
| Bernard A. Egwu | 2 | 0 | 0.34 |
| Zongqi Liang | 3 | 0 | 0.34 |
| Yubin Yan | 4 | 0 | 0.34 |