Computer Methods in Applied Mechanics and Engineering
Analysis of least squares finite element methods for the Stokes equations
Mathematics of Computation
Least-Squares Finite Element Method for the Stokes Problem with Zero Residual of Mass Conservation
SIAM Journal on Numerical Analysis
A least-squares approach based on a discrete minus one inner product for first order systems
Mathematics of Computation
First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II
SIAM Journal on Numerical Analysis
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
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The first order least squares finite element method is an alternative numerical procedure to standard Galerkin methods for the solution of partial differential equations. Its advantages are mainly the resulting symmetric positive definite matrices and the inherent numerical stability. Several first order formulations were proposed for the incompressible Navier-Stokes equations and for the equations of linear elasticity. Here we analyse which of these methods could provide an efficient and accurate tool for the solution of fluid-structure interaction problems. It seems that the combination of inherent least squares stability and high order ansatz functions is very promising.