MULTI-DIMENSIONAL EXPANSION BASES
This chapter considers the extension of the one-dimensional formulation to two and three dimensions by the development of expansion bases in standard regions such as triangles or rectangles in two dimensions, and tetrahedrons, prisms, pyramids, and hexahedrons in three dimensions. The construction of these bases uses a unified approach for the development of computationally efficient expansions. The modal basis is formulated as solutions to a generalized Sturm-Liouville problem. Optimal nodal points, the so-called Fekete points, the electrostatic points on a simplex, and related approximation results, are also presented. The exercises at the end of the chapter target construction of multi-dimensional elemental matrices.
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