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Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
We present a new family of stabilized methods for the Stokes problem. The focus of the paper is on the lowest order velocity-pressure pairs. While not LBB compliant, their simplicity and attractiveExpand
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Least-Squares Finite Element Methods
Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general settings,Expand
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A stabilized finite element method for the Stokes problem based on polynomial pressure projections
A new stabilized finite element method for the Stokes problem is presented. The method is obtained by modification of the mixed variational equation by using local L2 polynomial pressure projections.Expand
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Finite Element Methods of Least-Squares Type
We consider the application of least-squares variational principles to the numerical solution of partial differential equations. Our main focus is on the development of least-squares finite elementExpand
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Principles of Mimetic Discretizations of Differential Operators
Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework forExpand
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Analysis of least squares finite element methods for the Stokes equations
In this paper we consider the application of least-squares principles to the approximate solution of the Stokes equations cast into a first-order velocity-vorticity-pressure system. Among the mostExpand
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On stabilized finite element methods for the Stokes problem in the small time step limit
Recent studies indicate that consistently stabilized methods for unsteady incompressible flows, obtained by a method of lines approach may experience difficulty when the time step is small relativeExpand
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  • Open Access
On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles
Least-squares finite element methods for first-order formulations of the Poisson equation are not subject to the inf-sup condition and lead to stable solutions even when all variables areExpand
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On the Finite Element Solution of the Pure Neumann Problem
This paper considers the finite element approximation and algebraic solution of the pure Neumann problem. Our goal is to present a concise variational framework for the finite element solution of theExpand
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Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
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 onExpand
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