Adaptive least-squares finite element approximations to Stokes equations

•Adaptive least-squares methods are used to solve the Stokes equations.•Velocity–pressure–stress and velocity–vorticity–pressure formulations are used.•Mesh redistribution for planar and 4-to-1 contraction flow problems are developed.•Lower-order basis functions in all variables are used in least-squares methods.•Hybrid meshes of regular and graded grids are used to reduce the grid effects.

This paper is concerned with adaptive least-squares methods for Stokes equations based on velocity–pressure–stress and velocity–vorticity–pressure formulations. To capture the Stokes flow region, an adaptive algorithm based on mesh redistribution is developed for a nonlinear weighted least-squares functional. A redistribution approach is considered to generate the optimal grids. Model problems considered are the flow past a planar channel and a 4-to-1 contraction problems. Numerical results of model problems illustrating the efficiency of the proposed scheme are presented.