LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS

DOI10.1142/S0218202512500601zbMath1263.65112OpenAlexW2084441538MaRDI QIDQ4917963

Lijun Yi, Ben Qi Guo

Publication date: 3 May 2013

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202512500601

zbMATH Keywords

finite element method\(h-p\) versionlocal Chebyshev projection-interpolation operators

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (5)

Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method ⋮ Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. III: Inverse approximation theorems ⋮ Approximation of the derivatives of solutions in a normalized domain for 2D solids using the PIES method ⋮ $H^2$-Stable Polynomial Liftings on Triangles ⋮ Reprint of ``Construction of polynomial extensions in two dimensions and application to the \(h\)-\(p\) finite element method

Cites Work

• The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions
• Optimal error estimate of a projection based interpolation for the \(p\)-version approximation in three dimensions
• Direct and inverse error estimates for finite elements with mesh refinements
• The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version
• The optimal convergence of the \(h\)-\(p\) version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains
• 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 $h-p$ version of the boundary element method on polygonal domains with quasiuniform meshes
• Mixedhp-DGFEM for Incompressible Flows
• 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
• Discontinuoushp-Finite Element Methods for Advection-Diffusion-Reaction Problems
• 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
• The Optimal Convergence of theh‐pVersion of the Finite Element Method with Quasi‐Uniform Meshes
• 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
• \(hp\)-discontinuous Galerkin time stepping for parabolic problems

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