On the sharpness of certain local estimates for ¹ projections into finite element spaces: influence of a re-entrant corner
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In a plane polygonal domain with a reentrant corner, this article considered a homogeneous Dirichlet problem for Poisson's equation and the corresponding Galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi-uniform triangulations with the diameter of each element.Abstract:
In a plane polygonal domain with a reentrant corner, consider a homogeneous Dirichlet problem for Poisson's equation -Au = f with f smooth and the corresponding Galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi-uniform (uniformly regular) triangulations with the diameter of each element compara-read more
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A posteriori estimation and adaptive control of the pollution error in the h‐version of the finite element method
TL;DR: In this paper, the authors studied the pollution-error in the h-version of the finite element method and its effect on the quality of the local error indicators in the interior of the mesh.
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Well-posedness and Regularity for the Elasticity Equation with Mixed Boundary Conditions on Polyhedral Domains and Domains with Cracks
Anna L. Mazzucato,Victor Nistor +1 more
TL;DR: In this article, a regularity result for the anisotropic linear elasticity equation with mixed displacement and traction boundary conditions on a curved polyhedral domain was established. But the results were not extended to other strongly elliptic systems and higher dimensions.
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Multigrid methods for the computation of singular solutions and stress intensity factors I: corner singularities
TL;DR: The Poisson equation −Δu=f with homogeneous Dirichlet boundary condition on a two-dimensional polygonal domain Ω with cracks is considered and multigrid methods for the computation of singular solutions and stress intensity factors using piecewise linear functions are analyzed.
References
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Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Journal ArticleDOI
Interior estimates for Ritz-Galerkin methods
Joachim A. Nitsche,A. H. Schatz +1 more
TL;DR: In this article, it was shown that the error in an interior domain 2 can be estimated with the best order of accuracy that is possible locally for the subspaces used plus the error of a weaker norm over a slightly larger domain which measures the effects from outside of the domain Q.
Journal ArticleDOI
Maximum norm estimates in the finite element method on plane polygonal domains. I
A. H. Schatz,L. B. Wahlbin +1 more
TL;DR: In this article, the authors considered the model Dirichlet problem on a plane polygonal domain and derived the rate of convergence estimates in the maximum norm, up to the boundary, are given locally.