Adaptive Computation with Splines on Triangulations with Hanging Vertices

It is shown how computational methods based on Bernstein–Bezier methods for polynomial splines on triangulations can be carried over to compute with splines on triangulations with hanging vertices. Allowing triangulations with hanging vertices provides much more flexibility than using ordinary triangulations and allows for simple adaptive algorithms based on local refinements. The use of these techniques is illustrated for two application areas of splines—namely, function fitting and the solution of boundary value problems.