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REGULARITY AND NUME...
REGULARITY AND NUMERICAL APPROXIMATION OF FRACTIONAL ELLIPTIC DIFFERENTIAL EQUATIONS ON COMPACT METRIC GRAPHS
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- Bolin, David (författare)
- King Abdullah University of Science and Technology (KAUST)
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- Kovacs, Mihaly, 1977 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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Kumar, Vivek (författare)
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- Simas, Alexandre B. (författare)
- King Abdullah University of Science and Technology (KAUST)
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(creator_code:org_t)
- 2024
- 2024
- Engelska.
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Ingår i: Mathematics of Computation. - 1088-6842 .- 0025-5718. ; 93:349, s. 2439-2472
- Relaterad länk:
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https://research.cha...
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https://doi.org/10.1...
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https://gup.ub.gu.se...
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Abstract
Ämnesord
Stäng
- The fractional differential equation L(beta)u = f posed on a compact metric graph is considered, where beta > 0 and L = kappa(2) - del(a del ) is a second order elliptic operator equipped with certain vertex conditions and sufficiently smooth and positive coefficients kappa, a. We demonstrate the existence of a unique solution for a general class of vertex conditions and derive the regularity of the solution in the specific case of Kirchhoff vertex conditions. These results are extended to the stochastic setting when f is replaced by Gaussian white noise. For the deterministic and stochastic settings under generalized Kirchhoff vertex conditions, we propose a numerical solution based on a finite element approximation combined with a rational approximation of the fractional power L-beta. For the resulting approximation, the strong error is analyzed in the deterministic case, and the strong mean squared error as well as the L-2( Gamma x Gamma )error of the covariance function of the solution are analyzed in the stochastic setting. Explicit rates of convergences are derived for all cases. Numerical experiments for L = kappa(2) - del, kappa > 0 are performed to illustrate the results.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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