Given a rectangular box which has been split into 24 tetrahedra, we show how to construct a C1 macroelement using polynomial pieces of degree 6.

The mixed finite element scheme of the Stokes problem with pressure stabilization is analyzed for the cross-grid Pk−Pk−1 elements, k≥ 1, using discontinuous pressures. The P+ k −Pk−1 elements are also analyzed. We prove the stability of the scheme using the macroelement technique. The order of convergence follows from the standard theory of mixed methods. The macroelement technique can also be ...

We give a self-contained presentation of our macroelement technique for verifying the stability of finite element discretizations of Navier-Stokes equations in the velocity-pressure formulation. The results are also presented in form suitable for the non-mathematical reader.

An accurate evaluation of the non-linear behavior of masonry structural elements in existing buildings still represents a complex issue that rigorously requires non-linear finite element strategies difficult to apply to real large structures. Nevertheless, for the static and seismic assessment of existing structures, involving the contribution of masonry materials, engineers need reliable and e...

We develop a method for the analysis of mixed finite element methods for the Stokes problem in the velocity-pressure formulation. A technical "macroelement condition", which is sufficient for the classical Babuska-Brezzi inequality to be valid, is introduced. Using this condition,we are able to verify the stability, and optimal order of convergence, of several known mixed finite element methods.

Following a general analysis of convergence for the finite element solution of the stream function formulation of the Navier-Stokes equation in bounded regions of the plane, an algorithm for pressure recovery is presented. This algorithm, which is easy to implement, is then analyzed and conditions ensuring optimality of the approximation are given. An application is made to a standard conformin...

In this paper, a locally stabilized finite element formulation of the Stokes problem is analyzed. A macroelement condition which is sufficient for the stability of (locally stabilized) mixed methods based on a piecewise constant pressure approximation is introduced. By satisfying this condition, the stability of the Q\Pq, quadrilateral, and the P\-Pq triangular element, can be established.

We consider the mixed finite element approximation of axisymmetric Stokes problem (ASP) on a bounded polygonal domain in rz-plane. Standard stability results methods do not apply due to singular coefficients differential operator and or vanishing weights associated function spaces. develop new analysis these weighted spaces, propose macroelement conditions that are sufficient ensure well-posedn...

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...