Curved Isoparametric Boundary Elements For Cube Root Singularities
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In four previous papers, Henshell and Shaw%, Lynn and Ingraffea^, Mason* and Mason^ have defined isoparametric boundary elements for r^ type singularities at end points on lines, exterior points on lines, end points on curves and exterior points on curves, using quadratic, quadratic, cubic and quartic elements, respectively. We extend this idea here to develop curved isoparametric elements of degrees 5 and 6 (quintic and sextic), respectively, for end point and exterior point singularities of r^ type. This involves the solution by Newton's method, using a continuation method over a family of curves, of a small system of nonlinear equations.