| Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
|---|---|---|
| Page(s) | S3 - S28 | |
| DOI | https://doi.org/10.1051/m2an/2020022 | |
| Published online | 26 February 2021 | |
Numerical approximations for a fully fractional Allen–Cahn equation
IMAS – CONICET and Departamento de Matemática, FCEyN – Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires, Argentina
* Corresponding author: fbersetche@dm.uba.ar
Received:
29
March
2019
Accepted:
30
March
2020
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 Γ-convergence theory.
Mathematics Subject Classification: 65R20 / 65M60 / 35R11
Key words: Fractional Laplacian / Caputo derivative / semilinear evolution problems
© EDP Sciences, SMAI 2021
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