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Least-square finite element method for the Stokes problem with zero residual of mass conservation. (English) Zbl 0890.76036

A modified least-squares finite element method (LSFEM) is proposed to solve the two-dimensional problem in vorticity-velocity-pressure variables. The method enforces a near zero residual of mass conservation, i.e. the divergence of the velocity is nearly zero at every point of the discretization. Essentially, the authors use the Lagrange multiplier strategy. The method leads to symmetric matrices, thus the conjugate gradient method is suited to solve the finite dimensional problem. Some numerical experiments concerning the flow around a circular cylinder moving in a narrow channel are displayed. They show that the mass is nearly conserved everywhere.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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