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

DOI10.1016/j.jat.2013.05.001zbMath1382.65399OpenAlexW2083124319MaRDI QIDQ390540

Ivo M. Babuška, Ben Qi Guo

Publication date: 8 January 2014

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2013.05.001

zbMATH Keywords

algebraic approximationoptimal rate of convergenceJacobi-weighted Sobolev spacesdirect and inverse approximation theoremJacobi weightsJacobi-weighted Besov spacesthe \(p\)-version of finite element method

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) Error bounds for boundary value problems involving PDEs (65N15) 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

Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation, Interpolation in Jacobi-weighted spaces and its application to a posteriori error estimations of the \(p\)-version of the finite element method, Fast algorithms for the multi-dimensional Jacobi polynomial transform, Direct and inverse theorems of the approximation of functions by algebraic polynomials and splines in the norms of the Sobolev space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
• The optimal rate of convergence of the \(p\)-version of the boundary element method in two dimensions
• Equilibrated residual error estimates are \(p\)-robust
• Generalized Jacobi polynomials/functions and their applications
• Direct and inverse error estimates for finite elements with mesh refinements
• Elliptic problems in domains with piecewise smooth boundaries
• On the \(L_ 2\) error for the \(p\)-version of the finite element method over polygonal domains
• On best error bounds for approximation by piecewise polynomial functions
• An additive Schwarz preconditioner for \(p\)-version boundary element approximation of the hypersingular operator in three dimensions
• The optimal convergence of the \(h\)-\(p\) version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains
• Introduction to Finite Element Analysis
• Local Jacobi Operators and Applications to thep-Version of Finite Element Method in Two Dimensions
• Approximation Theory for the P-Version of the Finite Element Method in Three Dimensions Part II: Convergence of thePVersion of the Finite Element Method
• Regularity of the Solution of Elliptic Problems with Piecewise Analytic Data. Part I. Boundary Value Problems for Linear Elliptic Equation of Second Order
• Efficient Preconditioning for thep-Version Finite Element Method in Two Dimensions
• Thepandh-pVersions of the Finite Element Method, Basic Principles and Properties
• 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
• The Approximation of Solutions of Elliptic Boundary-Value Problems via the p-Version of the Finite Element Method
• 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
• 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
• The generalized finite element method
• On residual-based a posteriori error estimation in hp-FEM