Hierarchical quadrilateral elements in field analysis

Hierarchical forms of serendipitous quadrilateral elements offer the possibility of ad hoc specification of higher order elements in areas of special interest. Three hierarchical elements are discussed. It is found that the first type of hierarchy, for linear and quadratic elements, respectively yields significant error reductions, albeit at the expense of additional variables. These hierarchies can be imposed a posteriori without alteration of the mesh structure, thus increasing the accuracy in the required regions. A second type of hierarchy examined for a linear element, does not offer worthwhile improvements for the given class of boundary coefficients