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Stabilization of Low-order Mixed Finite Elements for the Stokes Equations

- P. Bochev, C. R. Dohrmann, M. Gunzburger
- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 1 June 2004

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 attractive… Expand

Least-Squares Finite Element Methods

- P. Bochev, M. Gunzburger
- Computer Science, Mathematics
- Applied mathematical sciences
- 23 March 2009

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

A stabilized finite element method for the Stokes problem based on polynomial pressure projections

- C. R. Dohrmann, P. Bochev
- Mathematics
- 20 September 2004

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

Finite Element Methods of Least-Squares Type

- P. Bochev, M. Gunzburger
- Computer Science, Mathematics
- SIAM Rev.
- 1 December 1998

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 element… Expand

Principles of Mimetic Discretizations of Differential Operators

- P. Bochev, J. H. Hyman
- Computer Science
- 2006

Compatible discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. We provide a common framework for… Expand

Analysis of least squares finite element methods for the Stokes equations

- P. Bochev, M. Gunzburger
- Mathematics
- 1 October 1994

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 most… Expand

On stabilized finite element methods for the Stokes problem in the small time step limit

- P. Bochev, M. Gunzburger, R. Lehoucq
- Mathematics
- 10 February 2007

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 relative… Expand

On Least-Squares Finite Element Methods for the Poisson Equation and Their Connection to the Dirichlet and Kelvin Principles

- P. Bochev, M. Gunzburger
- Mathematics, Computer Science
- SIAM J. Numer. Anal.
- 2005

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 are… Expand

On the Finite Element Solution of the Pure Neumann Problem

- P. Bochev, R. Lehoucq
- Computer Science, Mathematics
- SIAM Rev.
- 2005

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 the… Expand

Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations

- P. Bochev
- Mathematics
- 1 October 1997

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… Expand