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

Author:
Hsueh-Chen Lee   Tsu-Fen Chen  


Journal:
Computers & Mathematics with Applications


Issue Date:
2010


Abstract(summary):

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.[All rights reserved Elsevier].


Page:
215-224


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