Study of Superconvergence by a Computer-Based Approach: Superconvergence of theGradient of the Displacement, The Strain and Stress in Finite Element Solutions for Plane Elasticity

摘要

In another paper, we addressed the problem of existence of superconvergencepoints by a computer-based proof and we gave a detailed study of the superconvergence points for the components of the gradient in finite element solutions for Laplace's and Poisson's equations. Here we employ the same approach to study the superconvergence for the gradient of the displacement, the strain and the stress for finite element solutions of the equations of plane elasticity. We give the superconvergence points for the components of the gradient of the displacement, the strain and stress for meshes of triangles and squares of degree p, 1 < or = p < or = 4. For the meshes of triangles we investigated the effect of the topology of the mesh by considering four mesh-patterns which typically occur in practical meshes, while in the case of square elements we studied the effect of the element-type (tensor-product, serendipity or other).