Métodos numéricos para problemas no locales de evolución
This work introduces and analyzes a finite element scheme forevolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time weconsider is employed to represent memory effects, while a nonlocal differentiation...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/80087 |
| Acceso en línea: | http://hdl.handle.net/11336/80087 |
| Access Level: | acceso abierto |
| Palabra clave: | Laplaciano Fraccionario Derivada de Caputo Método de Elementos Finitos https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | This work introduces and analyzes a finite element scheme forevolution problems involving fractional-in-time and in-space differentiation operators up to order two. The left-sided fractional-order derivative in time weconsider is employed to represent memory effects, while a nonlocal differentiation operator in space accounts for long-range dispersion processes. We discusswell-posedness and obtain regularity estimates for the evolution problems under consideration. The discrete scheme we develop is based on piecewise linearelements for the space variable and a convolution quadrature for the time component. We illustrate the method?s performance with numerical experimentsin one- and two-dimensional domains. |
|---|