Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk
DOI10.1090/mcom/3645zbMath1480.65355OpenAlexW3136590395MaRDI QIDQ4999470
Zhongqiang Zhang, Zhimin Zhang, Zhao-peng Hao, Hui-yuan Li
Publication date: 7 July 2021
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/mcom/3645
Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Rate of convergence, degree of approximation (41A25) Representation and superposition of functions (26B40) Fractional partial differential equations (35R11)
Related Items (6)
Cites Work
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- The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Ten equivalent definitions of the fractional Laplace operator
- Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions
- An \(O(N \log ^{2}N)\) alternating-direction finite difference method for two-dimensional fractional diffusion equations
- Hardy inequalities for fractional integrals on general domains
- A spectral model for two-dimensional incompressible fluid flow in a circular basin. I: Mathematical formulation
- Spectra, signless Laplacian and Laplacian spectra of complementary prisms of graphs
- A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
- Numerical approximation of the integral fractional Laplacian
- Generalized Zernike or disc polynomials
- Fractional centered difference scheme for high-dimensional integral fractional Laplacian
- What is the fractional Laplacian? A comparative review with new results
- Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations
- Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains
- Error estimates of spectral Galerkin methods for a linear fractional reaction-diffusion equation
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- Regularity theory and high order numerical methods for the (1D)-fractional Laplacian
- Fast polynomial transforms based on Toeplitz and Hankel matrices
- Behavior of Solutions of 2D Quasi-Geostrophic Equations
- A Simple Solver for the Fractional Laplacian in Multiple Dimensions
- Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations
- Spectral Approximation on the Unit Ball
- Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
- Eigenvalues of the fractional Laplace operator in the unit ball
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