Augmented Lagrangian and Galerkin least-squares methods for membrane contact

Convergence analyses of Galerkin least - squares methods

Symmetric advective-di usive forms of the Stokes and incompressible Navier-Stokes equations are presented. The Galerkin least-squares method for advective-di usive equations is used for both systems and is related to other stabilized methods previously studied. The presentation reveals that the convergence analysis for advective-di usive equations, as applied before to a linearized form of the ...

Stabilized and Galerkin Least Squares Formulations

We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving p...

Practical Augmented Lagrangian Methods

for all x ∈ IR, λ ∈ IR, μ ∈ IR +. PHR-based Augmented Lagrangian methods for solving (1) are based on the iterative (approximate) minimization of Lρ with respect to x ∈ Ω, followed by the updating of the penalty parameter ρ and the Lagrange multipliers approximations λ and μ. The most popular practical Augmented Lagrangian method gave rise to the Lancelot package [24, 25, 26]. Lancelot does not...

Galerkin Least Squares Hp-fem for the Stokes Problem Galerkin Least Squares Hp-fem Pour Le Probl Eme De Stokes

A stabilized mixed hp Finite Element Method (FEM) of Galerkin Least Squares type for the Stokes problem in polygonal domains is presented and analyzed. It is proved that for equal order velocity and pressure spaces this method leads to exponential rates of convergence provided that the data is piecewise analytic. R esum e: Nous etudions la version hp d'une m ethode d' el ements nis mixte, stabi...

Least-Squares Galerkin Methods for Parabolic Problems II: The Fully Discrete Case and Adaptive Algorithms