Nonconforming Finite Element Analysis for a Plate Contact Problem

Han, Weimin; Wang, Lie-heng

doi:10.1137/s0036142901390731

Cited by 20 publications

(13 citation statements)

References 11 publications

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“…In order to characterize the solution of the variational inequality problem (2.3), we recall the following theorem due to Han and Wang [7]. Define the set Λ by Λ = {µ ∈ L ∞ (S) : |µ| 1 a.e.…”

Section: Plate Contact Problemmentioning

confidence: 99%

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Wang

2014

Journal of Numerical Mathematics

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In this paper, we deal with the discontinuous Galerkin finite element method for the plate contact problem with the frictional boundary conditions. The weak formulation is the variational inequality problem of the second kind. In virtue of the special discrete variational formulation, the error estimate in the broken H 2 norm is derived between the discontinuous approximation solution and the exact solution.

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Section: Plate Contact Problemmentioning

confidence: 99%

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Wang

2014

Journal of Numerical Mathematics

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“…Error analysis for some non-conforming finite element methods in solving an EVI of the first kind arising in unilateral problem, and an EVI of the second kind arising in a plate contact problem can be found in [228] and [116], respectively.…”

Section: A Signorini Frictionless Contact Problemmentioning

confidence: 99%

Theoretical Numerical Analysis

Atkinson¹,

Han²

2009

Texts in Applied Mathematics

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“…In this article, we propose and analyze the

C^{0} IP

method for a fourth‐order variational inequality of the second kind arising in frictional plate bending problem. The error analysis in has been derived with

H^{3} (Ω)

regularity of the exact solution of the continuous problem. But in general, the solution of the nonlinear partial differential equations have limited regularity.…”

Section: Introductionmentioning

confidence: 99%

A C⁰ interior penalty method for a fourth‐order variational inequality of the second kind

Gudi

Porwal

2015

Numerical Methods Partial

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In this article, we propose a C0 interior penalty ( C 0 I P ) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 36–59, 2016

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Nonconforming Finite Element Analysis for a Plate Contact Problem

Cited by 20 publications

References 11 publications

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Theoretical Numerical Analysis

A C⁰ interior penalty method for a fourth‐order variational inequality of the second kind

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Nonconforming Finite Element Analysis for a Plate Contact Problem

Cited by 20 publications

References 11 publications

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Discontinuous Galerkin finite element method for plate contact problem with frictional boundary conditions

Theoretical Numerical Analysis

A C0 interior penalty method for a fourth‐order variational inequality of the second kind

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A C⁰ interior penalty method for a fourth‐order variational inequality of the second kind