C*-convergence in the finite element method

In this paper a family of higher-order quadrilaterals for the Þnite element analysis of plane elasticity problems are developed, using the displacement method formulation. The number of nodes and the number of elements are Þxed, and reÞnement is achieved by adding derivatives of the nodal displacements as degrees of freedom at the nodes. It is shown that a higher rate of convergence is achieved compared with existing h- and p-versions of the Þnite element method. Applications to stress concentration and stress singularity are presented and the condition number is checked