Spectral method on quadrilaterals

DOI10.1090/S0025-5718-10-02329-XzbMath1207.65141OpenAlexW2094663607MaRDI QIDQ3160738

Hong-Li Jia, Ben-yu Guo

Publication date: 8 October 2010

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-10-02329-x

zbMATH Keywords

numerical resultsheat equationerror boundsPoisson equationspectral methodinterior domainsquadrilateralexterior problemsorthogonal approximation

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) Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

Related Items (22)

A spectral method for fourth-order mixed inhomogeneous boundary value problem in three dimensions ⋮ Legendre spectral method for solving mixed boundary value problems on rectangle ⋮ Generalized Jacobi approximation in multiple dimensions and its applications ⋮ A Petrov-Galerkin spectral method for fourth-order problems ⋮ A novel spectral method and error analysis for fourth-order equations in a spherical region ⋮ An efficient finite-element method and error analysis for the fourth-order elliptic equation in a circular domain ⋮ Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems on polygons ⋮ An efficient spectral method and rigorous error analysis based on dimension reduction scheme for fourth order problems ⋮ A triangular spectral element method for elliptic and Stokes problems ⋮ A spectral method for solving nonhomogeneous Neumann boundary value problems on quadrilaterals ⋮ A multi-domain spectral-Galerkin method for the Neumann problem on quadrilaterals ⋮ A novel spectral method and error estimates for fourth-order problems with mixed boundary conditions in a cylindrical domain ⋮ An \(H^m\)-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues ⋮ Pseudospectral method for quadrilaterals ⋮ Composite spectral method for exterior problems with polygonal obstacles ⋮ Some progress in spectral methods ⋮ Unnamed Item ⋮ Spectral element method for mixed inhomogeneous boundary value problems of fourth order ⋮ Jacobi and Laguerre quasi-orthogonal approximations and related interpolations ⋮ An efficient finite element method and error analysis for fourth order problems in a spherical domain ⋮ Spectral method for vorticity-stream function form of Navier-Stokes equations with slip boundary conditions ⋮ Spectral method for fourth-order problems on quadrilaterals

Cites Work

• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• Error analysis of spectral method on a triangle
• Composite Laguerre-Legendre spectral method for exterior problems
• Variational discretization of elliptic boundary value problems.
• Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
• Optimal spectral-Galerkin methods using generalized Jacobi polynomials
• Composite generalized Laguerre-Legendre spectral method with domain decomposition and its application to Fokker-Planck equation in an infinite channel
• Spectral Methods and Their Applications
• Spectral Methods
• Spectral Methods
• Approximation Theory for the p-Version of the Finite Element Method in Three Dimensions. Part 1: Approximabilities of Singular Functions in the Framework of the Jacobi-Weighted Besov and Sobolev Spaces
• Spectral/hp Element Methods for Computational Fluid Dynamics
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