First-order system least squares for second-order partial differential equations: part I
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
The Discrete First-Order System Least Squares: The Second-Order Elliptic Boundary Value Problem
SIAM Journal on Numerical Analysis
Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II
SIAM Journal on Numerical Analysis
Pseudospectral Least-Squares Method for the Second-Order Elliptic Boundary Value Problem
SIAM Journal on Numerical Analysis
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A spectral collocation approximation of first-order system least squares for incompressible Stokes equations was analyzed in Kim et al. (2004) [12], and finite element approximations for incompressible Navier-Stokes equations were developed in Bochev et al. (1998,1999) [9,10]. The aim of this paper is to analyze the first-order system least-squares pseudo-spectral method for incompressible Navier-Stokes equations. The paper will be an extension of the result in Kim et al. (2004) [12] to the Navier-Stokes equations. Our least-squares functional is defined by the sum of discrete spectral norms of a first-order system of equations corresponding to the Navier-Stokes equations based on Legendre-Gauss-Lobatto points. We show its ellipticity and continuity over an appropriate product space, and spectral convergences of discretization errors are derived in the H^1-norm and the L^2-norm in each variable. Finally, we present some numerical examples.