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 L 2-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 L 2-norm error convergence in all unknowns. Numerical solutions of the flow pass through a 4 to 1 contraction channel will also be considered. © 2009 Elsevier Ltd. All rights reserved.
Lee, H. C., & Chen, T. F. (2010). A nonlinear weighted least-squares finite element method for Stokes equations. Computers and Mathematics with Applications, 59(1), 215–224. https://doi.org/10.1016/j.camwa.2009.08.033