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A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators

  • Petr N. VabishchevichEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

Abstract

A boundary value problem for a fractional power \(0< \varepsilon < 1\) of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when \(\varepsilon \rightarrow 0\). It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. The numerical results are presented for a model two-dimensional boundary value problem with a fractional power of an elliptic operator. Our work focuses on the solution of the boundary value problem with \(0 < \varepsilon \ll 1\).

Keywords

Computational Grid Elliptic Operator Fractional Power Finite Element Discretizations Singularly Perturb 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was supported by the Russian Foundation for Basic Research (projects 14-01-00785, 15-01-00026).

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Nuclear Safety InstituteMoscowRussia
  2. 2.North-Eastern Federal UniversityYakutskRussia

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