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- W4298013764 abstract "We study the numerical approximation of a time dependent equation involving fractional powers of an elliptic operator $L$ defined to be the unbounded operator associated with a Hermitian, coercive and bounded sesquilinear form on $H^1_0(Omega)$. The time dependent solution $u(x,t)$ is represented as a Dunford Taylor integral along a contour in the complex plane. The contour integrals are approximated using sinc quadratures. In the case of homogeneous right-hand-sides and initial value $v$, the approximation results in a linear combination of functions $(z_qI-L)^{-1}vin H^1_0(Omega)$ for a finite number of quadrature points $z_q$ lying along the contour. In turn, these quantities are approximated using complex valued continuous piecewise linear finite elements. Our main result provides $L^2(Omega)$ error estimates between the solution $u(cdot,t)$ and its final approximation. Numerical results illustrating the behavior of the algorithms are provided." @default.
- W4298013764 created "2022-10-01" @default.
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- W4298013764 date "2016-07-26" @default.
- W4298013764 modified "2023-09-24" @default.
- W4298013764 title "The Approximation of Parabolic Equations Involving Fractional Powers of Elliptic Operators" @default.
- W4298013764 doi "https://doi.org/10.48550/arxiv.1607.07832" @default.
- W4298013764 hasPublicationYear "2016" @default.
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