Journal ArticleDOI
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
Reads0
Chats0
TLDR
In this paper, finite element methods of least-squares type for the stationary, incompressible Navier-Stokes equations in two and three dimensions were studied and optimal error estimates for conforming finite element approximations and analysis of some nonstandard boundary conditions were obtained.Abstract:
In this paper we study finite element methods of least-squares type for the stationary, incompressible Navier--Stokes equations in two and three dimensions. We consider methods based on velocity-vorticity-pressure form of the Navier--Stokes equations augmented with several nonstandard boundary conditions. Least-squares minimization principles for these boundary value problems are developed with the aid of the Agmon--Douglis--Nirenberg (ADN) elliptic theory. Among the main results of this paper are optimal error estimates for conforming finite element approximations and analysis of some nonstandard boundary conditions. Results of several computational experiments with least-squares methods which illustrate, among other things, the optimal convergence rates are also reported.read more
Citations
More filters
Book
Least-Squares Finite Element Methods
TL;DR: This paper focuses on theoretical and practical aspects of least-square finite element methods and includes discussions of what issues enter into their construction, analysis, and performance.
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
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
TL;DR: In this paper, a least-squares functional for the generalized Stokes equations was developed by adding a pressure term in the continuity equation, which yields optimal discretization error estimates for finite element spaces in an H1 product norm appropriately weighted by the Reynolds number.
Journal ArticleDOI
Spectral/ hp least-squares finite element formulation for the Navier-Stokes equations
J. P. Pontaza,J. N. Reddy +1 more
TL;DR: In this paper, the Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model.
Journal ArticleDOI
Space-time coupled spectral/ hp least-squares finite element formulation for the incompressible Navier-Stokes equations
J. P. Pontaza,J. N. Reddy +1 more
TL;DR: In this article, the effects of space and time are coupled, resulting in a true space-time least-squares minimization procedure, as opposed to a space time decoupled formulation where a least square minimisation procedure is performed in space at each time step.
References
More filters
Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
Book
Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms
TL;DR: This paper presents the results of an analysis of the "Stream Function-Vorticity-Pressure" Method for the Stokes Problem in Two Dimensions and its applications to Mixed Approximation and Homogeneous Stokes Equations.
Journal ArticleDOI
High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
U Ghia,K.N Ghia,C. T. Shin +2 more
TL;DR: The vorticity-stream function formulation of the two-dimensional incompressible NavierStokes equations is used to study the effectiveness of the coupled strongly implicit multigrid (CSI-MG) method in the determination of high-Re fine-mesh flow solutions.
Journal ArticleDOI
Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
Book
Introduction to partial differential equations
TL;DR: The Introduction to Partial Differential Equations (IDEQE) as discussed by the authors is the most widely used partial differential equation (PDE) formalism for algebraic partial differential equations.