Two-level schemes of Cauchy problem method for solving fractional powers of elliptic operators

DOI10.1016/j.camwa.2019.08.012zbMath1446.65062OpenAlexW2971161290WikidataQ127317577 ScholiaQ127317577MaRDI QIDQ2192557

Petr N. Vabishchevich, Raimondas Čiegis

Publication date: 17 August 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2019.08.012

zbMATH Keywords

finite element approximationelliptic operatorfractional power of an operatorstability of difference schemestwo-level schemes

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Padé approximation (41A21) Fractional partial differential equations (35R11)

Related Items (6)

A survey on numerical methods for spectral space-fractional diffusion problems ⋮ Neumann fractional diffusion problems: BURA solution methods and algorithms ⋮ Numerical identification of order of the fractional time derivative in a subdiffusion model ⋮ High-Order Two and Three Level Schemes for Solving Fractional Powers of Elliptic Operators ⋮ Splitting schemes for non-stationary problems with a rational approximation for fractional powers of the operator ⋮ Some methods for solving equations with an operator function and applications for problems with a fractional power of an operator

Cites Work

• Unnamed Item
• Unnamed Item
• Volume constrained 2-phase segmentation method utilizing a linear system solver based on the best uniform polynomial approximation of \(x^{- 1/2}\)
• A PDE approach to fractional diffusion: a posteriori error analysis
• Ten equivalent definitions of the fractional Laplace operator
• Numerically solving an equation for fractional powers of elliptic operators
• Turbulence and diffusion. Scaling versus equations
• Reformulation of elasticity theory for discontinuities and long-range forces
• A PDE approach to fractional diffusion in general domains: a priori error analysis
• Rational Approximation to the Fractional Laplacian Operator in Reaction-Diffusion Problems
• Nonlocal Continuum Field Theories
• Optimal solvers for linear systems with fractional powers of sparse SPD matrices
• $hp$-Finite Elements for Fractional Diffusion
• Numerical approximation of fractional powers of elliptic operators
• Numerical methods for fractional diffusion

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