Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees
type: Item
instance of: scholarly article
title: Exponential convergence of \(hp\)-FEM for elliptic problems in polyhedra: mixed boundary conditions and anisotropic polynomial degrees
zbMATH Open document ID: 1402.65166
author: Dominik Schötzau
author: Christoph Schwab
published in: Foundations of Computational Mathematics
publication date: 2018-08-10T00:00:00Z
review text: The authors consider \(hp\)-version finite element methods on geometric meshes consisting of hexahedral elements for linear, second-order elliptic boundary value problems in axiparallel polyhedral domains. Exponential rates of convergence are proved. The results extend and generalize the ones of the authors' previous work [Math. Models Methods Appl. Sci. 25, No. 9, 1617--1661 (2015; Zbl 1322.65099)] which dealt with homogeneous Dirichlet boundary conditions and uniform isotropic polynomial degrees to mixed Dirichlet-Neumann boundary conditions and to anisotropic hexahedra. \(H^1\)-conforming quasi-interpolation operators with \(N\) degrees of freedom are constructed. Exponential consistency bounds \(\exp (-b\root 5 \of {N})\) for piecewise analytic functions with singularities at edges, vertices and interfaces of boundary conditions are proved.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6916111
zbMATH Keywords: second-order elliptic problems in polyhedra
zbMATH Keywords: mixed boundary conditions
zbMATH Keywords: \(hp\)-FEM
zbMATH Keywords: anisotropic polynomial degrees
zbMATH Keywords: exponential convergence
MaRDI profile type: Publication
Wikidata QID: Q115605987
full work available at URL: s10208-017-9349-9
OpenAlex ID: W2596142527
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DOI: 10.1007/S10208-017-9349-9
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description: scientific article; zbMATH DE number 6916111