Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method

DOI10.1016/j.cam.2013.09.053zbMath1278.65176OpenAlexW2052048024MaRDI QIDQ390476

Jianming Zhang, Ben Qi Guo

Publication date: 8 January 2014

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2013.09.053

zbMATH Keywords

Sobolev spacesconvolutionliftingpolynomial extensioncontinuous operator\(p\) and \(h\)-\(p\) version FEM

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (2)

A posteriori error estimates for primal hybrid finite element methods applied to Poisson problem ⋮ $H^2$-Stable Polynomial Liftings on Triangles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An extension theorem for polynomials on triangles
• A preconditioner for the \(h\)-\(p\) version of the finite element method in two dimensions
• Local Jacobi Operators and Applications to thep-Version of Finite Element Method in Two Dimensions
• Polynomial Liftings on a Tetrahedron and Applications to the h-p Version of the Finite Element Method in Three Dimensions
• Stable and Compatible Polynomial Extensions in Three Dimensions and Applications to thepandh-pFinite Element Method
• Approximation Theory for the P-Version of the Finite Element Method in Three Dimensions Part II: Convergence of thePVersion of the Finite Element Method
• The $h-p$ version of the finite element method with quasiuniform meshes
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• The Schwarz Algorithm for Spectral Methods
• Thep-Version of the Finite Element Method
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Direct and Inverse Approximation Theorems for the p-Version of the Finite Element Method in the Framework of Weighted Besov Spaces. Part I: Approximability of Functions in the Weighted Besov Spaces
• DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS
• LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS
• The Optimal Convergence of theh‐pVersion of the Finite Element Method with Quasi‐Uniform Meshes

This page was built for publication: Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method