A \(C^1\) Petrov-Galerkin method and Gauss collocation method for 1D general elliptic problems and superconvergence

DOI10.3934/dcdsb.2020327zbMath1465.65128arXiv2002.02266OpenAlexW3094858006MaRDI QIDQ2026598

Waixiang Cao, Lueling Jia, Zhimin Zhang

Publication date: 20 May 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.02266

zbMATH Keywords

superconvergenceJacobi polynomialsHermite interpolationPetrov-Galerkin methodsGauss collocation methods\(C^1\) elements

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) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (4)

Superconvergence and postprocessing of the continuous Galerkin method for nonlinear Volterra integro-differential equations ⋮ Superconvergent postprocessing of the \(C^1\)-conforming finite element method for fourth-order boundary value problems ⋮ Superconvergence Analysis of $C^m$ Finite Element Methods for Fourth-Order Elliptic Equations I: One Dimensional Case ⋮ A $C^1$ Conforming Petrov--Galerkin Method for Convection-Diffusion Equations and Superconvergence Analysis over Rectangular Meshes

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