On the \(L_ 2\) error for the \(p\)-version of the finite element method over polygonal domains

DOI10.1016/0045-7825(92)90165-GzbMath0762.65058OpenAlexW2074866744MaRDI QIDQ1205644

S. Singh

Publication date: 1 April 1993

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(92)90165-g

zbMATH Keywords

finite element methodnumerical experimentserror estimationconvergence ratePoisson equation\(h\)-version\(p\)- version\(L\)-shaped membranenonconvex domain with re-entrant corners

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (8)

Discontinuous Galerkin solutions for elliptic problems on polygonal grids using arbitrary-order Bernstein-Bézier functions ⋮ Unlocking the secrets of locking: finite element analysis in planar linear elasticity ⋮ A parallel adaptive strategy for \(hp\) finite element computations ⋮ Construction of equilibrated singular basis functions without a priori knowledge of analytical singularity order ⋮ 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 ⋮ \(p\)-version of mixed finite element methods for Stokes-like problems ⋮ Error estimates and adaptive finite element methods ⋮ Some a priori error estimates with respect to \(H^{\theta}\) norms, \(0 <\theta < 1\), for the \(h\)-extension of the finite element method in two dimensions

Cites Work

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• The p- and h-p versions of the finite element method. An overview
• Finite element methods: Principles for their selection
• On computing the pressure by the \(p\) version of the finite element method for Stokes problem
• Some Error Estimates for the p-Version of the Finite Element Method
• On the Sharpness of Certain Local Estimates for $\overset{\circ}{H}^1$ Projections into Finite Element Spaces: Influence of a Reentrant Corner
• Polynomial approximation of some singular functions
• The Optimal Convergence Rate of the p-Version of the Finite Element Method

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