  Isogeometric Analysis (IgA) is a spline based approach to the numerical
solution of partial differential equations. There are two major issues that IgA
was designed to address. The first issue is the exact representation of domains
stemming from Computer Aided Design (CAD) software. In practice, this can be
realized only with multi-patch IgA, often in combination with trimming or
similar techniques. The second issue is the realization of high-order
discretizations (by increasing the spline degree) with numbers of degrees of
freedom comparable to low-order methods. High-order methods can deliver their
full potential only if the solution to be approximated is sufficiently smooth;
otherwise, adaptive methods are required. In the last decades, a zoo of local
refinement strategies for splines has been developed. The authors think that
many of these approaches are a burden to implement efficiently and impede the
utilization of recent advances that rely on tensor-product splines, e.g.,
concerning matrix assembly and preconditioning. The implementation seems to be
particularly cumbersome in the context of multi-patch IgA. Our approach is to
moderately increase the number of patches and to utilize different grid sizes
on different patches. This allows reusing the existing code bases, recovers the
convergence rates of other adaptive approaches and increases the number of
degrees of freedom only marginally.
