The finite element solution of second order elliptic problems with the Newton boundary condition

Čermák, Libor

doi:10.21136/am.1983.104055

Cited by 5 publications

(2 citation statements)

References 7 publications

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“…Our approach is largely inspired by the papers [2,3] and uses the technical results obtained in [58]. We basically adapt their approach to our problem.…”

Section: Numerical Integration Error Estimatementioning

confidence: 99%

Isogeometric Analysis on V-reps: First results

Antolín

Buffa

Martinelli

2019

Computer Methods in Applied Mechanics and Engineering

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Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parameterization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justifies our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.

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“…Our approach is largely inspired by the papers [2,3] and uses the technical results obtained in [58]. We basically adapt their approach to our problem.…”

Section: Numerical Integration Error Estimatementioning

confidence: 99%

Isogeometric Analysis on V-reps: First results

Antolín

Buffa

Martinelli

2019

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…However, there are much fewer studies of error analysis in other norms or for other boundary value problems, which take into account domain perturbation. For example, [2,4] gave optimal L 2 -error estimates for a Robin boundary value problem.…”

Section: Introductionmentioning

confidence: 99%

Pointwise error estimates of linear finite element method for Neumann boundary value problems in a smooth domain

Kashiwabara

Kemmochi

2020

Numer. Math.

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Pointwise error analysis of the linear finite element approximation for −∆u + u = f in Ω, ∂nu = τ on ∂Ω, where Ω is a bounded smooth domain in R N , is presented. We establish O(h 2 | log h|) and O(h) error bounds in the L ∞ -and W 1,∞ -norms respectively, by adopting the technique of regularized Green's functions combined with local H 1 -and L 2 -estimates in dyadic annuli. Since the computational domain Ω h is only polyhedral, one has to take into account non-conformity of the approximation caused by the discrepancy Ω h = Ω. In particular, the so-called Galerkin orthogonality relation, utilized three times in the proof, does not exactly hold and involves domain perturbation terms (or boundary-skin terms), which need to be addressed carefully. A numerical example is provided to confirm the theoretical result.

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Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains

Gong

Liang²,

Xie³

2023

Adv Comput Math

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The finite element solution of second order elliptic problems with the Newton boundary condition

Abstract: Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 5 publications

References 7 publications

Isogeometric Analysis on V-reps: First results

Isogeometric Analysis on V-reps: First results

Pointwise error estimates of linear finite element method for Neumann boundary value problems in a smooth domain

Pointwise error estimates for linear finite element approximation to elliptic Dirichlet problems in smooth domains

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