Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry

In this paper we develop the isogeometric Bézier dual mortar method. It is based on Bézier extraction and projection and is applicable to any spline space which can be represented in Bézier form (i.e., NURBS, T-splines, LR-splines, etc.). The approach weakly enforces the continuity of the solution at patch interfaces and the error can be adaptively controlled by leveraging the refineability of the underlying slave dual spline basis without introducing any additional degrees of freedom. As a consequence, optimal higher-order convergence rates can be achieved without the need for an expensive shared master/slave segmentation step. We also develop weakly continuous geometry as a particular application of isogeometric Bézier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified Bézier extraction operators. As a result, multi-patch models can be processed in a solver directly without having to employ a mortaring solution strategy. We demonstrate the utility of the approach on several challenging benchmark problems.