Analysis of [H-1,L2,L2] first-order system least squares for the incompressible Oseen type equations

Authors:
Sang Dong Kim;Yong Hun Lee;Suh-Yuh Yang
Affiliations:
Department of Mathematics, Kyungpook National University, Taegu 702-701, South Korea;Department of Mathematics, Chonbuk National University, Chonju 561-756, South Korea;Department of Mathematics, National Central University, Chung-Li 32054, Taiwan
Venue:
Applied Numerical Mathematics
Year:
2005

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Abstract

This paper is devoted to the error analysis of least-squares finite element approximations to the stationary incompressible Oseen type equations with the homogeneous velocity boundary condition. With the vorticity as a new dependent variable, we consider two first-order system problems for the Oseen type equations in the velocity-vorticity-pressure and the velocity-vorticity-Bernoulli pressure formulations. The least-squares functional is defined in terms of the sum of the squared H-1 and L2 norms of the residual equations over a suitable product function space. The well-posedness of the proposed least-squares variational problem is shown. We then analyze the case where the H-1 norm in the least-squares functional is replaced by a discrete functional to make the computation feasible. Optimal error estimates for all unknowns are derived.