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Symmetric interior penalty Galerkin method for fractional-in-space Allen-Cahn equations / Martin Stoll, Hamdullah Yücel
VerfasserStoll, Martin ; Yücel, Hamdullah
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, August 18, 2015
Umfang1 Online-Ressource (25 Seiten = 2,21 MB) : Illustrationen, Diagramme
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 15-14
URNurn:nbn:de:gbv:3:2-64804 
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Symmetric interior penalty Galerkin method for fractional-in-space Allen-Cahn equations [2.21 mb]
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Abstract: 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.