Shape functions associated with inverse element formulations

Super-convergent element formulations in local co-ordinates are obtained using inverse strategies. In the inverse approach discretization errors of the element formulation are minimized leading to super-convergent solutions. In the development of the inverse element model, no shape functions are introduced and therefore the task of element transformation from local to global co-ordinates system remains a challenge. In this paper, a procedure is proposed to produce shape functions associated with the inverse element formulations via hierarchical polynomials. A membrane element formulation is developed using inverse strategy as an example and its associated shape functions are determined using hierarchical polynomials. Numerical results indicate higher accuracy of the developed model in global co-ordinates compared to the reported models in the literature for the same element.