Higher Order NEM and FEM Accuracy Comparison

The natural-element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the finite-element method (FEM) for first-order consistency approximations. However, higher order approximations in the NEM framework are not obtained straightforwardly. This paper addresses a method of constructing higher order approximations out of the standard first-order NEM shape functions. This process is achieved through the de Boor algorithm. Accuracy of the scheme is compared with FEM. Results show that in second-order approximations context the NEM is still able to provide better accuracies for a given number of degrees of freedom.