Convergence of the C* family of finite elements and problems associated with forcing continuity of the derivatives at the nodes

A C*-convergence algorithm for finite element analysis has been proposed by Bigdeli and Kelly (1997) and elements for the first three levels applied t o planar elasticity have been defined. The fourth level element for the new family is described in this paper and the rate of convergence for the C*-c onvergence algorithm is investigated numerically. The new family adds deriv atives of displacements as nodal variables and the number of nodes and elem ents can therefore be kept constant during refinement. A problem exists on interfaces where the derivatives are required to be discontinuous. This pro blem is addressed for curved boundaries and a procedure is suggested to res olve the excessive interelement continuity which occurs.