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BIT Numerical Mathematics

Erschienen in:

23.06.2020

Variational formulation for fractional inhomogeneous boundary value problems

verfasst von: Taibai Fu, Zhoushun Zheng, Beiping Duan

Erschienen in: BIT Numerical Mathematics | Ausgabe 4/2020

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Abstract

The steady state fractional convection diffusion equation with inhomogeneous Dirichlet boundary is considered. By utilizing standard boundary shifting trick, a homogeneous boundary problem is derived with a singular source term which does not belong to \(L^2\) anymore. The variational formulation of such problem is established, based on which the finite element approximation scheme is developed. Inf-sup conditions for both continuous case and discrete case are demonstrated thus the corresponding well-posedness is verified. Furthermore, rigorous regularity analysis for the solutions of both original equation and dual problem is carried out, based on which the error estimates for the finite element approximation are derived. Numerical results are presented to illustrate the theoretical analysis.

Vorheriger Artikel Symplectic dynamical low rank approximation of wave equations with random parameters

Nächster Artikel Inexact methods for the low rank solution to large scale Lyapunov equations

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Titel: Variational formulation for fractional inhomogeneous boundary value problems
verfasst von: Taibai Fu
Zhoushun Zheng
Beiping Duan
Publikationsdatum: 23.06.2020
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 4/2020
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-020-00812-5

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