A Singularly Perturbed Boundary Value Problems with Fractional Powers of Elliptic Operators
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 \(0 < \varepsilon \ll 1\).
KeywordsComputational Grid Elliptic Operator Fractional Power Finite Element Discretizations Singularly Perturb
This work was supported by the Russian Foundation for Basic Research (projects 14-01-00785, 15-01-00026).
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