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.
|Number of pages||20|
|Journal||Mathematical Methods in the Applied Sciences|
|State||Published - Jun 1999|