Second order overhauser elements for boundary element analysis

The original ideas of Overhauser are extended to create a new type of element for boundary element analysis. Three Lagrange interpolation polynomials are blended together in a quadratic fashion, resulting in a set of seven basis functions which are C1 continuous from element to element. Solutions to Laplace's equation in a simple geometry are used to demonstrate the accuracy of the solutions obtained with the new elements, for both smooth and rapidly varying solutions. These new elements also provide more accurate values for the tangential derivative of the solution at all points on the boundary.