A least-squares finite-element method for the Stokes equations with improved mass balances

✍ Scribed by X. Ye

• Book ID: 104353602
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 433 KB
• Volume: 38
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(99)00197-2

✦ Synopsis

We prove the convergence of a least-squares mixed finite-element method for the Stokes equations with zero residual of mass conservation. For the standard least squares mixed finiteelement method, the equations for continuity of mass, and momentum are minimized in a global sense. Therefore, the mass may not be conserved at every point of the discretization. Recently, in [1], a modified least squares finite-element method is developed to enforce near zero residual of mass conservation. This is achieved by attaching a discrete divergence free constrain to the standard least squares finite-element method, and as a consequence, the number of equations is increased. In this paper, we take a different approach to improve the conservation of mass and reduce the number of the equations. This method does not require LBB condition on the finite-dimensional subspaces and the resulting bilinear form is symmetric and positive definite. (~) 1999 Elsevier Science Ltd. All rights reserved.