Spurious-free shape functions of triangular and rectangular elements are described in this paper. Complete-type and incomplete-type shape functions of the triangular elements are discussed, and a series of shape functions including Lagrange-type and Serendipity-type functions of the rectangular elements are discussed, too. Unknowns which are incidental to the shape functions are classified according to nodes, edges, and face of the triangular or rectangular element. Intelligent elements are constructed by the nodes, edges, and face whose degrees are different. Spurious-free elements are proposed by establishment of degrees in nodes, edges, and face. Physical eigen values of resonant frequency in a waveguide are calculated by using the suprious-free finite element.
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