Error analysis of a weighted least-squares finite element method for 2-D incompressible flows in velocity-stress-pressure formulation

研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(Scopus)

摘要

In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Reimann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm.

原文???core.languages.en_GB???
頁(從 - 到)1637-1654
頁數18
期刊Mathematical Methods in the Applied Sciences
21
發行號18
DOIs
出版狀態已出版 - 12月 1998

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