Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the triangle

DOI10.1090/S0025-5718-09-02308-4zbMath1197.65176OpenAlexW2084540358MaRDI QIDQ3584841

Jie Shen, Hui-yuan Li

Publication date: 30 August 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-09-02308-4

zbMATH Keywords

Orthogonal polynomialserror estimateKoornwinder polynomialsJacobi-weighted Sobolev spacesspectral-Galerkin method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

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Cites Work

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• Error analysis of spectral method on a triangle
• Generalized Jacobi polynomials/functions and their applications
• Spectral methods for problems in complex geometries
• Spectral methods on triangles and other domains
• Spectral collocation on triangular elements
• Stable spectral methods for conservation laws on triangles with unstructured grids
• A triangular spectral element method; applications to the incompressible Navier-Stokes equations.
• Approximation on simplices with respect to weighted Sobolev norms
• Optimal spectral-Galerkin methods using generalized Jacobi polynomials
• A Legendre--Petrov--Galerkin and Chebyshev Collocation Method for Third-Order Differential Equations
• A Triangular Spectral Element Method Using Fully Tensorial Rational Basis Functions
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• Invariant Integration Formulas for the n-Simplex by Combinatorial Methods
• Spectral approximations on the triangle
• A new triangular and tetrahedral basis for high‐order (hp) finite element methods
• Spectral Methods
• Integration Formulas and Orthogonal Polynomials for Two Variables
• Spectral/hp Element Methods for Computational Fluid Dynamics