In appendix A there is a summary of the modal triangle basis proposed by Dubiner [16] and the tetrahedral basis proposed and investigated by Sherwin [30]. Also, we list the modal bases for the prism, pyramid and hexahedron suggested by Sherwin in [27] and with Karniadakis in [31]. In the following subsections we will examine the properties of the bases for the triangle and quadrilateral. We will also propose some modifications to the shape functions that will enhance efficiency for the quadrilateral and provide compatibility between a triangle and a nodal quadrilateral.
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