  A finite element scheme for an entirely fractional Allen-Cahn equation with
non-smooth initial data is introduced and analyzed. In the proposed nonlocal
model, the Caputo fractional in-time derivative and the fractional Laplacian
replace the standard local operators. Piecewise linear finite elements and
convolution quadratures are the basic tools involved in the presented numerical
method. Error analysis and implementation issues are addressed together with
the needed results of regularity for the continuous model. Also, the asymptotic
behavior of solutions, for a vanishing fractional parameter and usual
derivative in time, is discussed within the framework of the Gamma-convergence
theory.
