Isogeometric regular discretization for the Stokes problem

The inf-sup stability and optimal convergence of an isogeometric C 1 discretization for the Stokes problem are shown. In this discretization the velocities are the pushforward through the geometrical map of cubic C1 non-uniform rational B-spline (NURBS) functions and the pressures are the pushforward of quadratic C1 NURBS. This paper follows the work in Bazilevs et al. (2006, Math. Models Methods Appl. Sci., 16, 1031-1090) where the authors showed the numerical result of this discretization and proved the inf-sup stability for C0 NURBS functions. The use of more regular functions is useful to decrease the degrees of freedom and thus the computational cost. The analysis is performed by means of the Verfürth trick, the macro-element technique, some approximation properties and the inf-sup condition for tensor products of B-spline spaces. © 2010 The author.