  In this paper, we introduce the isoGeometric Residual Minimization (iGRM)
method. The method solves stationary advection-dominated diffusion problems. We
stabilize the method via residual minimization. We discretize the problem using
B-spline basis functions. We then seek to minimize the isogeometric residual
over a spline space built on a tensor product mesh. We construct the solution
over a smooth subspace of the residual. We can specify the solution subspace by
reducing the polynomial order, by increasing the continuity, or by a
combination of these. The Gramm matrix for the residual minimization method is
approximated by a weighted H1 norm, which we can express as Kronecker products,
due to the tensor-product structure of the approximations. We use the Gramm
matrix as a preconditional which can be applied in a computational cost
proportional to the number of degrees of freedom in 2D and 3D. Building on
these approximations, we construct an iterative algorithm. We test the residual
minimization method on several numerical examples, and we compare it to the
Discontinuous Petrov-Galerkin (DPG) and the Streamline Upwind Petrov-Galerkin
(SUPG) stabilization methods. The iGRM method delivers similar quality
solutions as the DPG method, it uses smaller grids, it does not require
breaking of the spaces, but it is limited to tensor-product meshes. The
computational cost of the iGRM is higher than for SUPG, but it does not require
the determination of problem specific parameters.
