The F-E-M test for convergence of nonconforming finite elements

The F-E-M-Test for Convergence of Nonconforming Finite Elements

Nonconforming Finite Elements for the Stokes Problem

A new stability result is obtained for the approximation of the stationary Stokes problem by nonconforming piecewise cubic approximations to the velocities and a discontinuous piecewise quadratic approximation to the pressure. The basic result is that for most reasonable meshes, these elements form a stable pair without the addition of quartic bubble functions (which had previously been added t...

Nonconforming Tetrahedral Mixed Finite Elements for Elasticity

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, an...

A Note on the Nonconforming Finite Elements for Elliptic Problems

In this paper, a class of rectangular finite elements for 2m-th-oder elliptic boundary value problems in n-dimension (m,n ≥ 1) is proposed in a canonical fashion, which includes the (2m−1)-th Hermite interpolation element (n = 1), the n-linear finite element (m = 1) and the Adini element (m = 2). A nonconforming triangular finite element for the plate bending problem, with convergent order O(h)...

A Class of Nonconforming Quadrilateral Finite Elements for Incompressible Flow∗

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works [9, 8, 4], we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e. the first order accuracy of the velocities in H-norm and the pressure ...