Symmetric interior penalty Galerkin method for fractional-in-space phase-field equations

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10.3934Math.2018.1.66.pdf

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2018-01-01

Author

Stoll, Martin
Yücel, Hamdullah

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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 sciences and engineering. However, the non-local nature of the fractional operators causes essential difficulties and challenges for numerical approximations. We here investigate the numerical solution of fractional-in-space phase-field models such as Allen-Cahn and Cahn-Hilliard 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.

Subject Keywords

Allen-Cahn/Cahn-Hilliard equations, Fractional diffusion, Contour integral method, Implicit-explicit methods, Discontinuous Galerkin methods

URI

https://hdl.handle.net/11511/30660

Journal

AIMS MATHEMATICS

DOI

https://doi.org/10.3934/math.2018.1.66

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

M. Stoll and H. Yücel, “Symmetric interior penalty Galerkin method for fractional-in-space phase-field equations,” AIMS MATHEMATICS, pp. 66–95, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30660.