Name
Title | ||
|---|---|---|
Unconditionally Optimal Error Estimates of a Linearized Galerkin Method for Nonlinear Time Fractional Reaction-Subdiffusion Equations. |
Abstract | ||
|---|---|---|
This paper is concerned with unconditionally optimal error estimates of linearized Galerkin finite element methods to numerically solve some multi-dimensional fractional reaction–subdiffusion equations, while the classical analysis for numerical approximation of multi-dimensional nonlinear parabolic problems usually require a restriction on the time-step, which is dependent on the spatial grid size. To obtain the unconditionally optimal error estimates, the key point is to obtain the boundedness of numerical solutions in the \(L^\infty \)-norm. For this, we introduce a time-discrete elliptic equation, construct an energy function for the nonlocal problem, and handle the error summation properly. Compared with integer-order nonlinear problems, the nonlocal convolution in the time fractional derivative causes much difficulties in developing and analyzing numerical schemes. Numerical examples are given to validate our theoretical results. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s10915-018-0642-9 | J. Sci. Comput. |
Keywords | Field | DocType |
Unconditionally optimal error estimates, Linearized Galerkin method, Nonlinear fractional reaction–subdiffusion equations, High-dimensional nonlinear problems | Nonlinear system,Grid size,Mathematical analysis,Convolution,Galerkin method,Finite element method,Fractional calculus,Mathematics,Elliptic curve,Parabola | Journal |
Volume | Issue | ISSN |
76 | 2 | 0885-7474 |
Citations | PageRank | References |
6 | 0.43 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dongfang Li | 1 | 106 | 15.34 |
| Jiwei Zhang | 2 | 34 | 3.15 |
| Z. Zhang | 3 | 240 | 39.29 |