  In this paper, we propose a novel computational implicit method, which we
call Isogeometric Residual Minimization (iGRM) with direction splitting. The
method mixes the benefits resulting from isogeometric analysis, implicit
dynamics, residual minimization, and alternating direction solver. We utilize
tensor product B-spline basis functions in space, implicit second order time
integration schemes, residual minimization in every time step, and we exploit
Kronecker product structure of the matrix to employ linear computational cost
alternating direction solver. We implement an implicit time integration scheme
and apply, for each space-direction, a stabilized mixed method based on
residual minimization. We show that the resulting system of linear equations
has a Kronecker product structure, which results in a linear computational cost
of the direct solver, even using implicit time integration schemes together
with the stabilized mixed formulation. We test our method on three
advection-diffusion computational examples, including model ``membrane''
problem, the circular wind problem, and the simulations modeling pollution
propagating from a chimney.
