A Stable Discontinuous Galerkin Based Isogeometric Residual Minimization for the Stokes Problem

We investigate a residual minimization (RM) based stabilized isogeometric finite element method (IGA) for the Stokes problem. Starting from an inf-sup stable discontinuous Galerkin (DG) formulation, the method seeks for an approximation in a highly continuous trial space that minimizes the residual measured in a dual norm of the discontinuous test space. We consider two-dimensional Stokes problems with manufactured solutions and the cavity flow problem. We explore the results obtained by considering highly continuous isogeometric trial spaces, and discontinuous test spaces. We compare by the Pareto front the resulting numerical accuracy and the computational cost, expressed by the number of floating-point operations performed by the direct solver algorithm.