Finite element approximations for fractional evolution problems.
Resumen:
This work introduces and analyzes a finite element scheme for evolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time we consider is employed to represent memory effects, while a nonlocal differentiation operator in space accounts for long-range dispersion processes. We discuss well-posedness and obtain regularity estimates for the evolution problems under consideration. The discrete scheme we develop is based on piecewise linear elements for the space variable and a convolution quadrature for the time component. We illustrate the method's performance with numerical experiments in one- and two-dimensional domains.
| 2018 | |
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Fractional Laplacian Caputo derivative Evolution problems |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/47682 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
