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 documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2019 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositório: | CONICET Digital (CONICET) |
| Idioma: | inglês |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/80087 |
| Acesso em linha: | http://hdl.handle.net/11336/80087 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Laplaciano Fraccionario Derivada de Caputo Método de Elementos Finitos https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | 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. |
|---|