Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation

DOI10.1007/s10444-021-09905-3zbMath1496.41003arXiv2006.00667OpenAlexW3118737023MaRDI QIDQ824312

Boying Wu, Li-Lian Wang, Wen-Jie Liu

Publication date: 15 December 2021

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.00667

zbMATH Keywords

optimal estimatesapproximation by Legendre polynomialsfractional Taylor formulafunctions with interior and endpoint singularities

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Best constants in approximation theory (41A44)

Related Items (7)

Pointwise error estimates and local superconvergence of Jacobi expansions ⋮ Analysis of Error Localization of Chebyshev Spectral Approximations ⋮ Bernstein-type constants for approximation of \(| x |^\alpha\) by partial Fourier-Legendre and Fourier-Chebyshev sums ⋮ Optimal error estimates for Chebyshev approximations of functions with endpoint singularities in fractional spaces ⋮ Error analysis of Fourier–Legendre and Fourier–Hermite spectral-Galerkin methods for the Vlasov–Poisson system ⋮ Jacobian spectral collocation method for spatio-temporal coupled Fokker-Planck equation with variable-order fractional derivative ⋮ New error bounds for Legendre approximations of differentiable functions

Cites Work

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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. III: Inverse approximation theorems
• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• On right fractional calculus
• On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities
• On the decay rate of Chebyshev coefficients
• Mathematical analysis II. Translated from the 4th and 6th Russian editions by Roger Cooke and Octavio T. Paniagua
• Functional analysis, Sobolev spaces and partial differential equations
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• 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
• The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version
• Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions
• Pointwise error estimate of the Legendre expansion: the known and unknown features
• A new and sharper bound for Legendre expansion of differentiable functions
• How much faster does the best polynomial approximation converge than Legendre projection?
• Optimal decay rates on the asymptotics of orthogonal polynomial expansions for functions of limited regularities
• A fractional fundamental lemma and a fractional integration by parts formula-applications to critical points of Bolza functionals and to linear boundary value problems
• Asymptotics of the generalized Gegenbauer functions of fractional degree
• Optimal spectral-Galerkin methods using generalized Jacobi polynomials
• Spectral Methods
• Foundations of Mathematical Analysis
• Some Extensions of W. Gautschi's Inequalities for the Gamma Function
• Spectral Methods for Time-Dependent Problems
• On Gamma Function Inequalities
• Spectral Methods and Their Applications
• Local Fractional Fokker-Planck Equation
• The Lebesgue-Stieltjes Integral
• 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
• DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS
• On the Convergence Rates of Gauss and Clenshaw--Curtis Quadrature for Functions of Limited Regularity
• Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces
• Bounded Variation and Around
• Is Gauss Quadrature Better than Clenshaw–Curtis?
• Spectral Methods
• On some inequalities for the gamma and psi functions

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