A least-squares finite element method for the Helmholtz equation
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Optimal least-squares finite element method for elliptic problems
Computer Methods in Applied Mechanics and Engineering
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
Least-squares mixed finite elements for second-order elliptic problems
SIAM Journal on Numerical Analysis
First-Order System Least Squares for Second-Order Partial Differential Equations: Part II
SIAM Journal on Numerical Analysis
A least-squares approach based on a discrete minus one inner product for first order systems
Mathematics of Computation
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
SIAM Journal on Numerical Analysis
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The div least-squares methods have been studied by many researchers for the second-order elliptic equations, elasticity, and the Stokes equations, and optimal error estimates have been obtained in the $H(\mathrm{div})\times H^1$ norm. However, there is no known convergence rate when the given data $f$ belongs only to $L^2$ space. In this paper, we will establish an optimal error estimate in the $L^2\times H^1$ norm with the given data $f\in L^2$ and, hence, fill a theoretical gap of least-squares methods. As a consequence of this estimate, we will provide a convergence analysis for the linearization process on solving Navier-Stokes equations, which uses the div least-squares method for solving the corresponding Stokes equations.