Finite element approximations for fractional evolution problems-Reference-Cited by-同舟云学术

Finite element approximations for fractional evolution problems

Published:2019-06-01 Issue:3 Volume:22 Page:767-794
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Acosta Gabriel¹,Bersetche Francisco M.¹,Borthagaray Juan Pablo¹

Affiliation:

1. IMAS - CONICET and Departamento de Matemática , FCEyN - Universidad de Buenos Aires, Ciudad Universitaria , Pabellón I (1428) , Buenos Aires , Argentina

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2019-0042/pdf

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