| Issue |
ESAIM: M2AN
Volume 52, Number 5, September–October 2018
|
|
|---|---|---|
| Page(s) | 1981 - 2001 | |
| DOI | https://doi.org/10.1051/m2an/2018033 | |
| Published online | 11 December 2018 | |
A C0-nonconforming quadrilateral finite element for the fourth-order elliptic singular perturbation problem
1
School of Mathematical Sciences, Dalian University of Technology,
Dalian
116024, P.R. China.
2
School of Software, Dalian University of Technology,
Dalian
116620, P.R. China.
* Corresponding author: mzhl@dlut.edu.cn
Received:
9
October
2017
Accepted:
15
May
2018
In this paper, a C0 nonconforming quadrilateral element is proposed to solve the fourth-order elliptic singular perturbation problem. For each convex quadrilateral Q, the shape function space is the union of S21(Q*) and a bubble space. The degrees of freedom are defined by the values at vertices and midpoints on the edges, and the mean values of integrals of normal derivatives over edges. The local basis functions of our element can be expressed explicitly by a new reference quadrilateral rather than by solving a linear system. It is shown that the method converges uniformly in the perturbation parameter. Lastly, numerical tests verify the convergence analysis.
Mathematics Subject Classification: 65N30
Key words: Singular perturbation problem / quadrilateral element / uniformly convergent
© EDP Sciences, SMAI 2018
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