Diagonalized Legendre spectral methods using Sobolev orthogonal polynomials for elliptic boundary value problems

DOI10.1016/j.apnum.2018.01.003zbMath1382.65424OpenAlexW2783213324MaRDI QIDQ1696838

Hui-yuan Li, Qing Ai, Zhong-qing Wang

Publication date: 15 February 2018

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.01.003

zbMATH Keywords

Neumann boundary value problemSobolev orthogonal polynomialsnumerical experimentHelmholtz equationssecond-order elliptic boundary value problemsDirichlet boundary value problemssingular perturbation problemsa posterior error estimatesLegendre spectral method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (9)

Hermite–Sobolev orthogonal functions and spectral methods for second- and fourth-order problems on unbounded domains ⋮ Legendre spectral element method for solving Volterra-integro differential equations ⋮ Unnamed Item ⋮ A Legendre dual-Petrov-Galerkin spectral element method for the Kawahara-type equations ⋮ Legendre spectral element method for solving sine-Gordon equation ⋮ Jacobi-Sobolev orthogonal polynomials and spectral methods for elliptic boundary value problems ⋮ A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation ⋮ Efficient Legendre dual-Petrov-Galerkin methods for odd-order differential equations ⋮ The error estimates of spectral methods for 1-dimension singularly perturbed problem

Cites Work

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• Sobolev orthogonal polynomials on product domains
• Spectral methods using generalized Laguerre functions for second and fourth order problems
• Spectral Methods
• Fast algorithms for discrete polynomial transforms
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Spectral Methods

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