✦ LIBER ✦

Stability of penalty finite-element methods for nonconforming problems

✍ Scribed by Graham F. Carey; Mehmet Utku

Publisher: John Wiley and Sons
Year: 1986
Tongue: English
Weight: 651 KB
Volume: 2
Category: Article
ISSN: 0749-159X
DOI: 10.1002/num.1690020103

No coin nor oath required. For personal study only.

✦ Synopsis

Penalty methods have been proposed as a viable method for enforcing interelement continuity constraints on nonconforming elements. Particularly for fourth-order problems in which C '-continuity leads to elements of high degree or complex composite elements, the use of penalty methods to enforce the C '-continuity constraint appears promising. In this study we demonstrate equivalence of the finite-ekment penalty method to a hybrid method and provide a stability analysis which implies that the penalty method is stable only if reduced integration of a certain order is used. Numerical experiments confirm that the penalty method fails if this condition is not met.

📜 SIMILAR VOLUMES

A nonconforming mixed finite element for

A nonconforming mixed finite element for second-order elliptic problems

✍ Mohamed Farhloul; And Michel Fortin 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB 👁 2 views

In a recent work, Hiptmair [Mathematisches Institut, M9404, 1994] has constructed and analyzed a family of nonconforming mixed finite elements for second-order elliptic problems. However, his analysis does not work on the lowest order elements. In this article, we show that it is possible to constru

Superconvergence of nonconforming finite

Superconvergence of nonconforming finite element method for the Stokes equations

✍ Xiu Ye 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 108 KB

This article derives a general superconvergence result for nonconforming finite element approximations of the Stokes problem by using a least-squares surface fitting method proposed and analyzed recently by Wang for the standard Galerkin method. The superconvergence result is based on some regularit

A stabilized discontinuous finite elemen

A stabilized discontinuous finite element method for elliptic problems

✍ Richard E. Ewing; Junping Wang; Yongjun Yang 📂 Article 📅 2002 🏛 John Wiley and Sons 🌐 English ⚖ 167 KB

## Abstract A new finite element method is proposed and analysed for second order elliptic equations using discontinuous piecewise polynomials on a finite element partition consisting of general polygons. The new method is based on a stabilization of the well‐known primal hybrid formulation by usin

Approximation and eigenvalue extrapolati

Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods

✍ Shanghui Jia; Hehu Xie; Xiaobo Yin; Shaoqin Gao 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 140 KB

## Abstract In this paper, we analyze the biharmonic eigenvalue problem by two nonconforming finite elements, __Q__ and __E Q__. We obtain full order convergence rate of the eigenvalue approximations for the biharmonic eigenvalue problem based on asymptotic error expansions for these two nonconform

Convergence and superconvergence analysi

Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction–diffusion problems

✍ Guoqing Zhu; Shaochun Chen 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 339 KB 👁 1 views

## Abstract The numerical approximation by a lower‐order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi‐optimal‐order error estimates are proved in the ε‐weighted __H__^1^‐norm valid uniformly, up to a

The stability of finite element methods

✍ Rüdiger Verfürth 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 805 KB