Adaptivity, trimming, patch gluing: the agenda for spline-based methods

In the last ten years the use of splines as a tool for the discretisation of partial differential equations has gained interests thanks to the advent of isogeometric analysis. For this class of methods, all robust and accurate techniques aiming at enhancing the flexibility of splines, while keeping their structure, are of paramount importance since the tensor product structure underlying spline constructions is far too restrictive in the context of approximation of partial differential equations (PDEs).

I will describe various approaches, from adaptivity with regular splines, to regular patch gluing and to trimming. Moreover, I will show applications and test benches involving large deformation problems with contact and quasi-incompressible materials.