In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted r...

A fully automatic mesher has been developed which is capable of generating both quadrilateral and triangular elements in 2-D and on surfaces using the advancing front algorithm. This allows the formation of meshes which range from being all-quad or nearly all-quad down to all-triangular. In mixed-element meshes, the number of tri elements present is dictated by the maximum allowable level of qu...

Automatic finite element mesh generation techniques have become commonly used tools for the analysis of complex, real-world models. All of these methods can, however, create distorted and even unusable elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. Smoothing (also referred to as mesh relaxation) is one such method, which repositions noda...

A new low order membrane nite element is presented. The element formulation is based on the variational principle of Hughes and Brezzi employing an independent rotation eld. In the present work nonconforming interpolation is used for the drill rotation eld. Both triangular and quadrilateral elements are considered. Combined with the Reissner-Mindlin plate bending element of O~ nate, Zarate and ...

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. Hence, several techniques have been developed to limit the gradient of the element size. However, the obtained discretizations do not always reproduce the prescribed size function. This is of the major importance for quadrilateral meshes, since they are much more constrained ...

This paper provides an error analysis for the Crank–Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier–Stokes problem, where the finite element space pair (Xh,Mh) for the approximation (uh, p n h) of the velocity u and the pressure p is constructed by the low-order finite ele...

In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 − P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtain...

We prove the optimal order of convergence for some two-dimensional finite element methods for the Stokes equations. First we consider methods of the Taylor-Hood type: the triangular Pi P2 element and the Qk Qk-\ > k ^ 2 , family of quadrilateral elements. Then we introduce two new low-order methods with piecewise constant approximations for the pressure. The analysis is performed using our macr...