The Construction of Basis Functions for Curved Elements in the Finite Element Method

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Abstract
Part basis (wedge) functions are constructed for plane triangular elements with two straight and one curved side, using ideas from three dimensional geometry. Such elements are desirable for regions with curved boundaries or interfaces. Lagrange interpolating functions which are in turn (i) linear, (ii) quadratic, and (iii) cubic along the straight sides of the triangle are considered. Curved elements which had previously been dealt with using isoparametric co-ordinates appear as special cases of this more general geometrical treatment. The ideas can be extended in a straightforward manner to deal with tetrahedral elements with three plane and one curved surface.

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