Jin, B;
Lazarov, R;
Zhou, Z;
(2016)
Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data.
Siam Journal On Scientific Computing
, 38
(1)
A146-A170.
10.1137/140979563.
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Abstract
We consider initial/boundary value problems for the subdiffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two fully discrete schemes based on the piecewise linear Galerkin finite element method in space and convolution quadrature in time with the generating function given by the backward Euler method/second-order backward difference method, and establish error estimates optimal with respect to the regularity of problem data. These two schemes are first- and second-order accurate in time for both smooth and nonsmooth data. Extensive numerical experiments for two-dimensional problems confirm the convergence analysis and robustness of the schemes with respect to data regularity. Read More: http://epubs.siam.org/doi/10.1137/140979563
| Type: | Article |
|---|---|
| Title: | Two fully discrete schemes for fractional diffusion and diffusion-wave equations with nonsmooth data |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/140979563 |
| Publisher version: | http://dx.doi.org/10.1137/140979563 |
| Language: | English |
| Additional information: | First Published in SIAM Journal on Scientific Computing in Volume 38, Issue 1 (2016), published by the Society of Industrial and Applied Mathematics (SIAM). Copyright © 2016 Society for Industrial and Applied Mathematics. |
| Keywords: | Fractional diffusion, diffusion wave, finite element method, convolution quadrature, error estimate |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1471667 |
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