Stabilization Of Low-Order Mixed Finite Elements For The Plane Elasticity Equations

In this paper, we present two stabilizationes of low-order mixed finite element for the Plane Elasticity problems. Despite low-order finite element spaces violate the LBB stability condition, their simplicity and attractive computational properties make them a popular choice in engineering practice. To counteract their lack of LBB stability, we use appropriate operators with suitable range spaces to represent the " deficiency", and use the corresponding formular to construct a stable variational problem. Our stabilized methods need not deal with higher order derivatives or the jump of edge-based data, and they lead to easy algebraic problems. So they have simple and convenient implementations, and our stabilized methods have good convergence.