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Least squares finite element methods for the Stokes and Navier-Stokes equations
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The article was published on 1994-07-18 and is currently open access. It has received 8 citations till now. The article focuses on the topics: Non-linear least squares & Least squares.read more
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Journal ArticleDOI
Finite Element Methods of Least-Squares Type
TL;DR: The use of least-squares principles leads to symmetric and positive definite algebraic problems and allows us to circumvent stability conditions such as the inf-sup condition arising in mixed methods for the Stokes and Navier--Stokes equations.
Journal ArticleDOI
Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I
TL;DR: In this article, a least-squares approach based on L2 norms was proposed to solve the Navier-Stokes equations in primitive variables. But this approach does not allow practical implementation, and these results are critical to the analysis of a practical least square method for the reduced system based on a discrete equivalent of the negative norm.
Journal ArticleDOI
A unified least-squares formulation for fluid-structure interaction problems
TL;DR: Cai et al. as mentioned in this paper proposed a mixed first-order least square formulation for the Navier-Stokes equations and the linear elastodynamics, which achieves the optimal convergence rate in all problem unknowns.
Least-Squares FEM: Literature Review
TL;DR: In this paper, the authors give an overview of the recent literature in the field of least square finite element methods and summarise the essential results and facts about the LSFEM.
DissertationDOI
Least-Squares Methods for the Solution of Fluid-Structure Interaction Problems
TL;DR: In this article, an alternative variational principle, the least squares finite element method, was tested with respect to its application for transient fluid-structure interaction problems, and the accurracy of different formulations which were proposed for the Navier-Stokes equations in literature was tested.
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