# A New Rotated Nonconforming Quadrilateral Element

@article{Meng2018ANR, title={A New Rotated Nonconforming Quadrilateral Element}, author={Zhaoliang Meng and Jintao Cui and Zhongxuan Luo}, journal={Journal of Scientific Computing}, year={2018}, volume={74}, pages={324-335} }

In this paper, a new nonparametric nonconforming quadrilateral finite element is introduced. This element takes the four edge mean values as the degrees of the freedom and the finite element space is a subspace of $$P_{2}$$P2. Different from the other nonparametric elements, the basis functions of this new element can be expressed explicitly without solving linear systems locally, which can be achieved by introducing a new reference quadrilateral. To evaluate the integration, a class of new…

## 6 Citations

AC0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem

- MathematicsESAIM: Mathematical Modelling and Numerical Analysis
- 2018

In this paper, aC0nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateralQ, the shape function space is the…

A new rotated nonconforming pyramid element

- MathematicsNumerical Methods for Partial Differential Equations
- 2019

In this paper, a new nonparametric nonconforming pyramid finite element is introduced. This element takes the five face mean values as the degrees of the freedom and the finite element space is a…

A note on a lowest order divergence‐free Stokes element on quadrilaterals

- MathematicsMathematical Methods in the Applied Sciences
- 2019

This short note reports a lowest order divergence‐free Stokes element on quadrilateral meshes. The velocity space is based on a P1 spline element over the crisscross partition of a quadrilateral, and…

Simple quadrature rules for a nonparametric nonconforming quadrilateral element

- MathematicsArXiv
- 2022

We introduce simple quadrature rules for the family of nonparametric nonconforming quadrilateral element with four degrees of freedom. Our quadrature rules are motivated by the work of Meng et al.…

Nonconforming polynomial mixed finite element for the Brinkman problem over quadrilateral meshes

- Mathematics, Computer ScienceComput. Math. Appl.
- 2018

Effect of numerical integration on a new rotated nonconforming quadrilateral element

- Journal of Computational and Applied Mathematics
- 2022

## References

SHOWING 1-10 OF 24 REFERENCES

P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems

- MathematicsSIAM J. Numer. Anal.
- 2003

A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions that consists of only piecewise linear polynomials that are continuous at the midpoints of edges.

New nonconforming finite elements on arbitrary convex quadrilateral meshes

- MathematicsJ. Comput. Appl. Math.
- 2016

A piecewise P2-nonconforming quadrilateral finite element

- Mathematics
- 2013

We introduce a piecewise P 2 -nonconforming quadrilateral finite element. First, we decompose a convex quadrilateral into the union of four triangles divided by its diagonals. Then the finite element…

A class of nonparametric DSSY nonconforming quadrilateral elements

- Mathematics
- 2013

A new class of nonparametric nonconforming quadrilateral finite elements is introduced which has the midpoint continuity and the mean value continuity at the interfaces of elements simul- taneously…

A non‐conforming piecewise quadratic finite element on triangles

- Computer Science, Mathematics
- 1983

It is shown in this paper that non-conforming finite elements on the triangle using second-degree polynomials can be easily built and used and that this element exhibits a very peculiar regularity property.

A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier–Stokes equations

- Mathematics
- 1999

Abstract:Recently, Douglas et al. [4] introduced a new, low-order, nonconforming rectangular element for scalar elliptic equations. Here, we apply this element in the approximation of each component…

A nonconforming quadrilateral element with maximal inf‐sup constant

- Computer Science
- 2014

A new nonconforming element is introduced for quadrilateral meshes designed to maximize the inf‐sup constant for a Stokes element pair and it is observed that the maximizing inf‐Sup constant results in efficiency of computing time.

Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

- Mathematics
- 1999

Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements…

Simple nonconforming quadrilateral Stokes element

- Physics
- 1992

A simple nonconforming quadrilateral Stokes element based on “rotated” multi-linear shape functions is analyzed. On strongly nonuniform meshes the usual parametric version of this element suffers…