Adaptive discontinuous Galerkin B-splines on parametric geometries

We treat numerical simulations on exact geometries by using a discontinuous Galerkin scheme with B-spline bases. That will be realized by the interior penalty form. The initial meshless geometry is constituted of large parametric blocks. We propose an a-posteriori error indicator based on the control points of the B-spline approximations. That enables an efficient adaptive local refinement. Discrete B-splines are used for cascading conjugate gradient iterations. In addition, we provide results on single patches in two and three dimensions.