A Least-Squares Mixed Finite Element for Quasi-Incompressible Elastodynamics

Least Squares Finite Element Methods for Viscous, Incompressible Flows

This paper is concerned with finite element methods of least-squares type for the approximate numerical solution of incompressible, viscous flow problems. Our main focus is on issues that are critical for the success of the finite element methods, such as decomposition of the Navier-Stokes equations into equivalent first-order systems, mathematical prerequisites for the optimality of the method...

Multilevel Boundary Functionals for Least-squares Mixed Finite Element Methods

For least-squares mixed nite element methods for the rst-order system formulation of second-order elliptic problems, a technique for the weak enforcement of boundary conditions is presented. This approach is based on least-squares boundary functionals which are equivalent to the H ?1=2 and H 1=2 norms on the trace spaces of lowest-order Raviart-Thomas elements for the ux and standard continuous...

Nonconforming elements in least-squares mixed finite element methods

In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated Q1 nonconforming element and the lowest-order ...

A Least Squares Spectral Element Method for Incompressible Flow Simulations

Least-Squares Finite Element Methods

Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general settings, the advantageous features of Rayleigh–Ritz methods such as the avoidance of discrete compatibility conditions and the production of symmetric and positive definite discrete systems. The methods are...