✦ LIBER ✦

Analysis of a two-stage least-squares finite element method for the planar elasticity problem

✍ Scribed by Suh-Yuh Yang; Ching L. Chang

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 163 KB
Volume: 22
Category: Article
ISSN: 0170-4214
DOI: 10.1002/(sici)1099-1476(199906)22:9<713::aid-mma972>3.0.co;2-n

No coin nor oath required. For personal study only.

✦ Synopsis

A new "rst-order formulation for the two-dimensional elasticity equations is proposed by introducing additional variables which, called stresses here, are the derivatives of displacements. The resulted stress}displacement system can be further decomposed into two dependent subsystems, the stress system and the displacement system recovered from the stresses. For constructing "nite element approximations to these subsystems with appropriate boundary conditions, a two-stage least-squares procedure is introduced. The analysis shows that, under suitable regularity assumptions, the rates of convergence of the least-squares approximations for all the unknowns are optimal both in the H-norm and in ¸-norm. Also, numerical experiments with various Poisson's ratios are examined to demonstrate the theoretical estimates.

📜 SIMILAR VOLUMES

A two-stage least-squares finite element

A two-stage least-squares finite element method for the stress-pressure-displacement elasticity equations

✍ Suh-Yuh Yang; Ching L. Chang 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 398 KB 👁 1 views

A new stress-pressure-displacement formulation for the planar elasticity equations is proposed by introducing the auxiliary variables, stresses, and pressure. The resulting first-order system involves a nonnegative parameter that measures the material compressibility for the elastic body. A two-stag

Implementation of a least-squares finite

Implementation of a least-squares finite element method for solving the Stokes problem with a parameter

✍ I. O. Arushanian; G. M. Kobelkov 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 62 KB 👁 1 views

The implementation of a least-squares finite element method for solving the generalized stationary Stokes problem (i.e. the Stokes problem with an additional term αu in the motion equation, where α is a big parameter and u is the velocity vector function) is considered. The basis of this method is t

Superconvergence analysis of least-squar

Superconvergence analysis of least-squares mixed finite element method for second-order non-self-adjoint two-point boundary value problems

✍ Bi, Chunjia ;Li, Likang 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 150 KB 👁 2 views

A least-squares mixed ®nite element method for the second-order non-self-adjoint two-point boundary value problems is formulated and analysed. Superconvergence estimates are developed in the maximum norm at Gaussian points and at Lobatto points.

Simulation of two-fluid flows by the lea

Simulation of two-fluid flows by the least-squares finite element method using a continuum surface tension model

✍ Jie Wu; Sheng-Tao Yu; Bo-Nan Jiang 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 286 KB 👁 2 views

In this paper a numerical procedure for simulating two-uid ows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols 1 and the Continuum Surface Force (CSF) model developed by Brackbill et al. 2 In the VOF method uids of di erent properties are identi

Error analysis of a weighted least-squar

Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity–stress–pressure formulation

✍ Suh-Yuh Yang 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 148 KB 👁 1 views

In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stre