Artículo
Numerical approximations for a fully fractional Allen-Cahn equation
Fecha de publicación:
04/2020
Editorial:
EDP Sciences
Revista:
Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique
ISSN:
0764-583X
e-ISSN:
2804-7214
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
Palabras clave:
CAPUTO DERIVATIVE
,
FRACTIONAL LAPLACIAN
,
SEMILINEAR EVOLUTION PROBLEMS
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Acosta Rodriguez, Gabriel; Mastroberti Bersetche, Francisco Vicente; Numerical approximations for a fully fractional Allen-Cahn equation; EDP Sciences; Esaim-mathematical Modelling And Numerical Analysis-modelisation Matheematique Et Analyse Numerique; 55; 4-2020; 1-26
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