The maximum angle condition is not necessary for convergence of the finite element method

We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition is only sufficient. In fact, finite element approximations may converge even though some dihedral angles of simplicial elements tend to π

Compatible smooth interpolation in triangles

AbstractBoolean sum smooth interpolation to boundary data on a triangle is described. Sufficient conditions are given so that the functions when pieced together form a CN−1(Ω) function over a triangular subdivision of a polygonal region Ω and the precision sets of the interpolation functions are derived. The interpolants are modified so that the compatibility conditions on the function which is interpolated can be removed and a C1 interpolant is used to illustrate the theory. The generation of interpolation schemes for discrete boundary data is also discussed

A marching method for computing intersection curves of two subdivision solids

This paper presents a marching method for computing intersection curves between two solids represented by subdivision surfaces of Catmull-Clark or Loop type. It can be used in trimming and boolean operations for subdivision surfaces. The main idea is to apply a marching method with geometric interpretation to trace the intersection curves. We first determine all intersecting regions, then find pairs of initial intersection points, and trace the intersection curves from the initial intersection points. Various examples are given to demonstrate the robustness and efficiency of our algorithm. © Springer-Verlag Berlin Heidelberg 2005