A nonlinear weighted least-squares finite element method for Stokes equations

The paper concerns a nonlinear weighted least-squares finite element method for the solutions of the incompressible Stokes equations based on the application of the least-squares minimization principle to an equivalent first order velocity–pressure–stress system. Model problem considered is the flow in a planar channel. The least-squares functional involves the L2L2-norms of the residuals of each equation multiplied by a nonlinear weighting function and mesh dependent weights. Using linear approximations for all variables, by properly adjusting the importance of the mass conservation equation and a carefully chosen nonlinear weighting function, the least-squares solutions exhibit optimal L2L2-norm error convergence in all unknowns. Numerical solutions of the flow pass through a 4 to 1 contraction channel will also be considered.