Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 403–419 |
| Journal / Publication | Journal of Scientific Computing |
| Volume | 80 |
| Issue number | 1 |
| Online published | 22 Mar 2019 |
| Publication status | Published - Jul 2019 |
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Abstract
A Newton linearized Galerkin finite element method is proposed to solve nonlinear time fractional parabolic problems with non-smooth solutions in time direction. Iterative processes or corrected schemes become dispensable by the use of the Newton linearized method and graded meshes in the temporal direction. The optimal error estimate in the L2 -norm is obtained without any time step restrictions dependent on the spatial mesh size. Such unconditional convergence results are proved by including the initial time singularity into concern, while previous unconditional convergent results always require continuity and boundedness of the temporal derivative of the exact solution. Numerical experiments are conducted to confirm the theoretical results.
Research Area(s)
- Linearized schemes, Optimal error estimates, Time fractional parabolic problems, Unconditional convergence
Citation Format(s)
Linearized Galerkin FEMs for Nonlinear Time Fractional Parabolic Problems with Non-smooth Solutions in Time Direction. / Li, Dongfang; Wu, Chengda; Zhang, Zhimin.
In: Journal of Scientific Computing, Vol. 80, No. 1, 07.2019, p. 403–419.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
