The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces

Previous papers have examined the method and accuracy of generating B-spline approximations to PDE surfaces; such approximations being obtained using the finite element method with appropriate B-spline basis functions as the basis. This paper looks at the use of multiple knots in the B-spline surface approximation to a PDE surface with a view to allowing discontinuities in the surface normal at certain locations. The method is applied to the surface of a yacht hull where an analytic solution is known, and hence comparison using approximations to the Euclidean and maximum norms can be made.