MACRO STOKES ELEMENTS ON QUADRILATERALS

被引：0

作者：

Neilan, Michael ^{[1
]}

Sap, Duygu ^{[1
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15226 USA

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2018年 / 15卷 / 4-5期

关键词：

Finite element analysis; divergence-free; quadrilateral mesh; FINITE-ELEMENTS; PIECEWISE POLYNOMIALS; MASS CONSERVATION; APPROXIMATION; SPACES; FAMILY; GRIDS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a pair of conforming and inf-sup stable finite element spaces for the two-dimensional Stokes problem yielding divergence-free approximations on general convex quadrilateral partitions. The velocity and pressure spaces consist of piecewise quadratic and piecewise constant polynomials, respectively. We show that the discrete velocity and a locally post-processed pressure solution are second-order convergent.

引用

页码：729 / 745

页数：17

共 50 条

[1] Composite mixed finite elements on plane quadrilaterals
Bendali, A.
Lahmar, N.
Numerical Methods for Partial Differential Equations, 1993, 9 (05) : 551 - 559
[2] Bilinear finite elements for shells:: Isoparametric quadrilaterals
Niemi, Antti H.
Pitkaranta, Juhani
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2008, 75 (02) : 212 - 240
[3] A new family of nonconforming finite elements on quadrilaterals
Li, Youai
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2015, 70 (04) : 637 - 647
[4] Direct serendipity and mixed finite elements on convex quadrilaterals
Todd Arbogast
Zhen Tao
Chuning Wang
Numerische Mathematik, 2022, 150 : 929 - 974
[5] Pseudo-conforming polynomial finite elements on quadrilaterals
Dubach, Eric
Luce, Robert
Thomas, Jean-Marie
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (10-11) : 1798 - 1816
[6] Direct serendipity and mixed finite elements on convex quadrilaterals
Arbogast, Todd
Tao, Zhen
Wang, Chuning
NUMERISCHE MATHEMATIK, 2022, 150 (04) : 929 - 974
[7] A note on a lowest order divergence-free Stokes element on quadrilaterals
Zhou, Xinchen
Meng, Zhaoliang
Fan, Xin
Luo, Zhongxuan
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (11) : 4008 - 4016
[8] Robust nonconforming polynomial finite elements over quadrilaterals
Zhou, Xinchen
Meng, Zhaoliang
Fan, Xin
Luo, Zhongxuan
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2021, 98 (04) : 758 - 782
[9] Brahmagupta quadrilaterals are lattice quadrilaterals
Marshall, Susan H.
Tortorelli, Brooke
INVOLVE, A JOURNAL OF MATHEMATICS, 2024, 17 (04):
[10] hp-approximation theory for BDFM and RT finite elements on quadrilaterals
Ainsworth, M
Pinchedez, K
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2003, 40 (06) : 2047 - 2068

← 1 2 3 4 5 →