ABSTRACT
In Chapter 4, we discussed the implementation of the finite element method in two dimensions with linear triangular elements defined by three nodes. To improve the accuracy of the interpolation and also account for the boundary curvature, we may discretize the solution domain into triangular or quadrilateral elements with curved edges defined by a higher number of nodes. In addition, we may approximate the solution over the individual elements isoparametrically or superparametrically using quadratic or high-order polynomial expansions expressed in nodal or modal form. Spectral element methods arise by judiciously deploying the element interpolation nodes at positions corresponding to optimal interpolation sets that are specific to the selected element type.
