Pointwise Mass Conservative Least Squares Isogeometric Analysis for Stokes Problem

Conventional least squares finite element method for incompressible flow does not enforce mass conservation in pointwise, i.e. the velocity field is not exactly divergence free. In this paper, we present a pointwise mass conservative least squares isogeometric analysis for the Stokes problem. The method utilizes high order smooth basis functions generated from non-uniform rational B-spline (NURBS). Pointwise divergence free velocity field is defined using stream function on each patch of computational domain. Velocity boundary conditions and cross patch continuity are enforced in least square sense. Numerical results are presented for flow past a large circular cylinder in a channel and flow over a backward facing step. The results show improvements on local and global mass conservation.