A $C^1$ Conforming Petrov--Galerkin Method for Convection-Diffusion Equations and Superconvergence Analysis over Rectangular Meshes

DOI10.1137/21m1391006zbMath1529.65118arXiv2103.07628OpenAlexW4210487040MaRDI QIDQ6172656

Zhimin Zhang, Waixiang Cao, Lueling Jia

Publication date: 20 July 2023

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.07628

zbMATH Keywords

superconvergenceJacobi polynomialsHermite interpolationPetrov-Galerkin methods\(C^1\)-conforming

Mathematics Subject Classification ID

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) Numerical interpolation (65D05)

Related Items

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, Superconvergence analysis of curlcurl-conforming elements on rectangular meshes, Nonconforming modified quasi-Wilson finite element method for convection-diffusion-reaction equation

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