In this study we consider parallel conjugate gradient solution of sparse systems arising from the least-squares mixed finite element method. Of particular interest are transport problems involving convection. The least-squares approach leads to a symmetric positive system and the conjugate gradient
Least-squares finite elements for fluid flow and transport
โ Scribed by G. F. Carey; A. I. Pehlivanov; Y. Shen; A. Bose; K. C. Wang
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 167 KB
- Volume
- 27
- Category
- Article
- ISSN
- 0271-2091
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โฆ Synopsis
The least-squares mixed ยฎnite element method is concisely described and supporting error estimates and computational results for linear elliptic (steady diffusion) problems are brieยฏy summarized. The extension to the stationary NavierยฑStokes problems for Newtonian, generalized Newtonian and viscoelastic ยฏuids is then considered. Results of numerical studies are presented for the driven cavity problem and for a stickยฑslip problem.
๐ SIMILAR VOLUMES
A least-squares approach is presented for implementing uniform strain triangular and tetrahedral รฟnite elements. The basis for the method is a weighted least-squares formulation in which a linear displacement รฟeld is รฟt to an element's nodal displacements. By including a greater number of nodes on t
The RLW equation is solved by a least-squares technique using linear space-time finite elements. In simulations of the migration of a single solitary wave this algorithm is shown to have higher accuracy and better conservation than a recent difference scheme based on cubic spline interpolation funct
Based on the Helmholtz decomposition of the transverse shear strain, Brezzi and Fortin in [7] introduced a three-stage algorithm for approximating the Reissner-Mindlin plate model with clamped boundary conditions and established uniform error estimates in the plate thickness. The first and third sta
This article studies a least-squares finite element method for the numerical approximation of compressible Stokes equations. Optimal order error estimates for the velocity and pressure in the H 1 are established. The choice of finite element spaces for the velocity and pressure is not subject to the
In this paper a numerical procedure for simulating two-uid ows is presented. This procedure is based on the Volume of Fluid (VOF) method proposed by Hirt and Nichols 1 and the Continuum Surface Force (CSF) model developed by Brackbill et al. 2 In the VOF method uids of di erent properties are identi