H-1 least-squares method for the velocity-pressure-stress formulation of Stokes equations
Applied Numerical Mathematics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Least-squares finite element models of two-dimensional compressible flows
Finite Elements in Analysis and Design
Journal of Computational Physics
Analysis of [H-1,L2,L2] first-order system least squares for the incompressible Oseen type equations
Applied Numerical Mathematics
On mass conservation in least-squares methods
Journal of Computational Physics
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational and Applied Mathematics
Higher-Order Gauss---Lobatto Integration for Non-Linear Hyperbolic Equations
Journal of Scientific Computing
A least-squares finite element method for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Analysis of a least-squares finite element method for the thin plate problem
Applied Numerical Mathematics
Weighted least-squares finite elements based on particle imaging velocimetry data
Journal of Computational Physics
Finite Elements in Analysis and Design - Special issue: The sixteenth annual Robert J. Melosh competition
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
The least-squares pseudo-spectral method for Navier-Stokes equations
Computers & Mathematics with Applications
Newton multigrid least-squares FEM for the V-V-P formulation of the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
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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.