Preprint No. MPIMD/15-14

Title: Symmetric Interior Penalty Galerkin Method For Fractional-In-Space Allen-Cahn Equations

Author(s): Martin Stoll, Hamdullah Yücel


Date: 2015-08-18


Fractional differential equations are becoming increasingly popular as a modelling tool to describe a wide range of non-classical phenomena with spatial heterogeneities throughout the applied science and engineering. However, the non-local nature of the fractional operators causes essential difficulties and challenges for numerical approximations. We here address an efficient approach to solve fractional-in-space Allen-Cahn equations via the contour integral method (CIM) for computing the fractional power of a matrix times a vector. Time discretization is performed by the first-and second-order implicit-explicit schemes with an adaptive time-step size approach, whereas spatial discretization is performed by a symmetric interior penalty Galerkin (SIPG) method. Several numerical examples are presented to illustrate the effect of the fractional power.


author = {Martin Stoll and Hamdullah Yücel},
title = {Symmetric Interior Penalty Galerkin Method For Fractional-In-Space Allen-Cahn Equations},
number = {MPIMD/15-14},
month = aug,
year = 2015,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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