Least-square finite elements for Stokes problem
Computer Methods in Applied Mechanics and Engineering
Least-squares finite element method for fluid dynamics
Computer Methods in Applied Mechanics and Engineering
Spectral simulation of an unsteady compressible flow past a circular cylinder
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Error analysis of some Galerkin least squares methods for the elasticity equations
SIAM Journal on Numerical Analysis
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
Analysis of Least-Squares Finite Element Methods for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
Finite Element Methods of Least-Squares Type
SIAM Review
Least-squares spectral elements applied to the Stokes problem
Journal of Computational Physics
Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
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We consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solid and fluid mechanics. For many of these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model. For instance, the use of least-squares principles leads to a variational unconstrained minimization problem where compatibility conditions between approximation spaces never arise. Furthermore, the resulting linear algebraic problem will have a symmetric positive definite coefficient matrix, allowing the use of robust and fast iterative methods for its solution. We find that the use of high p-levels is beneficial in least-squares based finite element models and present guidelines to follow when a low p-level numerical solution is sought. Numerical examples in the context of incompressible and compressible viscous fluid flows, plate bending, and shear-deformable shells are presented to demonstrate the merits of the formulations.