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Finite Element Approximation for the Fractional Eigenvalue Problem

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Abstract

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical experiments and compare our results with previous work by other authors.

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Acknowledgements

The authors would like to thank G. Grubb and R. Rodríguez for the valuable help they provided through clarifying discussions on the topic of this paper, and to F. Bersetche for improving the efficiency of the Matlab code employed.

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Authors and Affiliations

  1. IMAS - CONICET and Departamento de Matemática, FCEyN - Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina

    Juan Pablo Borthagaray & Sandra Martínez

  2. CONICET and UTDT, Departamento de Matemáticas y Estadística, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350, C1428BCW, Buenos Aires, Argentina

    Leandro M. Del Pezzo

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  1. Juan Pablo Borthagaray
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  2. Leandro M. Del Pezzo
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  3. Sandra Martínez
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Correspondence to Leandro M. Del Pezzo.

Additional information

Research of Juan Pablo Borthagaray has been partially supported by CONICET under Grant PIP 2014-2016 11220130100184CO.

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Borthagaray, J.P., Del Pezzo, L.M. & Martínez, S. Finite Element Approximation for the Fractional Eigenvalue Problem. J Sci Comput 77, 308–329 (2018). https://doi.org/10.1007/s10915-018-0710-1

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