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

DOI10.1137/040614803zbMath1115.65117OpenAlexW2146686865MaRDI QIDQ5470956

Ben Qi Guo

Publication date: 2 June 2006

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

Full work available at URL: https://doi.org/10.1137/040614803

zbMATH Keywords

finite element method\(p\)-versionthree dimensionsedge singularityvertex singularityvertex-edge singularityJacobi projectionJacobi-weighted Besov and Sobolev spaces

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Spectral method on quadrilaterals, 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, Convergence analysis of an energy based discontinuous Galerkin method for the wave equation in second-order form: \( h p\) version, Thehp-version of the boundary element method with quasi-uniform meshes in three dimensions, Optimal convergence estimates for the trace of the polynomial $L^{2}$-projection operator on a simplex, Analytic Regularity for the Incompressible Navier--Stokes Equations in Polygons, LOCAL CHEBYSHEV PROJECTION–INTERPOLATION OPERATOR AND APPLICATION TO THE h–p VERSION OF THE FINITE ELEMENT METHOD IN THREE DIMENSIONS, Local high-order regularization and applications to \(hp\)-methods, Superconvergence of the \(h\)-\(p\) version of the finite element method in one dimension, ℎ𝑝-Discontinuous Galerkin methods for the Helmholtz equation with large wave number