Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval (Q2027923)

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English	Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval	scientific article

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scholarly article

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title

Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval (English)

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Journal of Scientific Computing

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publication date

28 May 2021

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full work available at URL

https://arxiv.org/abs/2002.02330

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zbMATH Keywords

fractional diffusion equation

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Petrov-Galerkin

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Jacobi polynomials

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spectral method

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weighted Sobolev spaces

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MaRDI profile type

MaRDI publication profile

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cites work

Q5558293

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Regularity theory and high order numerical methods for the (1D)-fractional Laplacian

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Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces

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Image Denoising Methods. A New Nonlocal Principle

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Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation

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Generalized Jacobi functions and their applications to fractional differential equations

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Compact finite difference method for the fractional diffusion equation

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Theory and practice of finite elements.

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Regularity of the solution to 1-D fractional order diffusion equations

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Variational formulation for the stationary fractional advection dispersion equation

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Numerical approximation of the fractional Laplacian via \(hp\)-finite elements, with an application to image denoising

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On the fractional diffusion-advection-reaction equation in \(\mathbb{R}\)

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The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions

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Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces

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Error estimates of a spectral Petrov-Galerkin method for two-sided fractional reaction-diffusion equations

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Optimal Regularity and Error Estimates of a Spectral Galerkin Method for Fractional Advection-Diffusion-Reaction Equations

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Existence and Regularity of solutions to 1-D Fractional Order Diffusion Equations

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A simple finite element method for boundary value problems with a Riemann-Liouville derivative

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Variational formulation of problems involving fractional order differential operators

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A Petrov--Galerkin Finite Element Method for Fractional Convection-Diffusion Equations

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Spectral approximations to the fractional integral and derivative

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A mixed‐type Galerkin variational formulation and fast algorithms for variable‐coefficient fractional diffusion equations

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Numerical solution of the space fractional Fokker-Planck equation.

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Finite element approximation for a modified anomalous subdiffusion equation

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Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations

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A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative

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Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients

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Spectral element method with geometric mesh for two-sided fractional differential equations

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Finite difference approximations for fractional advection-dispersion flow equations

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Q4061445

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A second-order accurate numerical method for the two-dimensional fractional diffusion equation

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A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations

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Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations

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Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations

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Fractional Sturm-Liouville eigen-problems: theory and numerical approximation

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Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension

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An indirect finite element method for variable-coefficient space-fractional diffusion equations and its optimal-order error estimates

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Identifiers

zbMATH Open document ID

1465.65154

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Mathematics Subject Classification ID

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10.1007/S10915-020-01366-Y

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Sitelinks

Mathematics(1 entry)

mardi Publication:2027923