FEM for fractional evolution problems

J. P. BORTHAGARAY; G. ACOSTA; F. BERSETCHE

Strobl

Congreso; 30 Chemnitz FEM 2017; 2017

Chemnitz UT, Johann Radon Instiute

In this talk we introduce a finite element scheme for evolution problems involvingfractional-in-time and in-space differentiation operators up to order two. The left-sidedfractional-order derivative in time we consider is employed to represent memory effects,while a nonlocal differentiation operator in space accounts for long-range dispersionprocesses. We discuss well-posedness and obtain regularity estimates for the evolutionproblems under consideration. The discrete scheme we develop is based on piecewiselinear elements for the space variable and a convolution quadrature for the timecomponent. We present approximation error estimates for our method and illustrate itsperformance with numerical experiments in one- and two-dimensional domains.