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

@article{Park2003P1NonconformingQF, title={P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems}, author={Chunjae Park and Dongwoo Sheen}, journal={SIAM J. Numer. Anal.}, year={2003}, volume={41}, pages={624-640} }

A P1 -nonconforming quadrilateral finite element is introduced for second-order elliptic problems in two dimensions. Unlike the usual quadrilateral nonconforming finite elements, which contain quadratic polynomials or polynomials of degree greater than 2, our element consists of only piecewise linear polynomials that are continuous at the midpoints of edges. One of the benefits of using our element is convenience in using rectangular or quadrilateral meshes with the least degrees of freedom…

## 143 Citations

A New Rotated Nonconforming Quadrilateral Element

- MathematicsJ. Sci. Comput.
- 2018

Numerical results are shown to confirm the optimality of the convergence order for the second order elliptic problems and the Stokes problem.

P1-Nonconforming Quadrilateral Finite Volume Methods for the Semilinear Elliptic Equations

- MathematicsJ. Sci. Comput.
- 2012

Numerical results of the proposed finite volume methods with interpolated coefficients to solve the semilinear elliptic problems show its better performance than others.

Locally stabilized p1-nonconforming quadrilateral and hexahedral finite element methods for the Stokes equations

- MathematicsJ. Comput. Appl. Math.
- 2011

Numerical analysis for a new non-conforming linear finite element on quadrilaterals

- Computer Science
- 2006

A quadrilateral nonconforming finite element for linear elasticity problem

- MathematicsAdv. Comput. Math.
- 2008

The optimal convergence rate of the method is established in the broken $H^1$ energy and $L^2$-norms, and in particular, the convergence is uniform with respect to the Lamé parameter $\lambda$.

Nonconforming finite element methods on quadrilateral meshes

- Mathematics
- 2013

It is well known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in…

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…

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From the Publisher:
This book is particularly useful to graduate students, researchers, and engineers using finite element methods. The reader should have knowledge of analysis and functional…