TY - JOUR

T1 - Analysis of a two-stage least-squares finite element method for the planar elasticity problem

AU - Yang, Suh Yuh

AU - Chang, Ching L.

PY - 1999/6

Y1 - 1999/6

N2 - A new first-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 finite 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 H1-norm and in L2-norm. Also, numerical experiments with various Poisson's ratios are examined to demonstrate the theoretical estimates.

AB - A new first-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 finite 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 H1-norm and in L2-norm. Also, numerical experiments with various Poisson's ratios are examined to demonstrate the theoretical estimates.

UR - http://www.scopus.com/inward/record.url?scp=0032682483&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1099-1476(199906)22:9<713::AID-MMA972>3.0.CO;2-N

DO - 10.1002/(SICI)1099-1476(199906)22:9<713::AID-MMA972>3.0.CO;2-N

M3 - 期刊論文

AN - SCOPUS:0032682483

VL - 22

SP - 713

EP - 732

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 9

ER -