A Cubic H3-Nonconforming Finite Element

doi:10.1007/s42967-019-0009-8

Communications on Applied Mathematics and Computation ›› 2019, Vol. 1 ›› Issue (1): 81-100.doi: 10.1007/s42967-019-0009-8

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A Cubic H³-Nonconforming Finite Element

Jun Hu¹, Shangyou Zhang²

1. LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China;
2. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

收稿日期:2018-07-29 修回日期:2018-09-15 出版日期:2019-03-20 发布日期:2019-05-11
通讯作者: Jun Hu, Shangyou Zhang E-mail:hujun@math.pku.edu.cn;szhang@udel.edu
基金资助:
The first author is supported by the National Natural Science Foundation of China (Nos.11271035,91430213,11421101).

A Cubic H³-Nonconforming Finite Element

Jun Hu¹, Shangyou Zhang²

1. LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China;
2. Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA

Received:2018-07-29 Revised:2018-09-15 Online:2019-03-20 Published:2019-05-11
Contact: Jun Hu, Shangyou Zhang E-mail:hujun@math.pku.edu.cn;szhang@udel.edu
Supported by:
The first author is supported by the National Natural Science Foundation of China (Nos.11271035,91430213,11421101).

摘要/Abstract

摘要： The lowest degree of polynomial for a finite element to solve a 2kth-order elliptic equation is k. The Morley element is such a finite element, of polynomial degree 2, for solving a fourth-order biharmonic equation. We design a cubic H³-nonconforming macro-element on two-dimensional triangular grids, solving a sixth-order tri-harmonic equation. We also write down explicitly the 12 basis functions on each macro-element. A convergence theory is established and verified by numerical tests.

关键词: Nonconforming macro-element, Minimum element, Tri-harmonic equation

Abstract: The lowest degree of polynomial for a finite element to solve a 2kth-order elliptic equation is k. The Morley element is such a finite element, of polynomial degree 2, for solving a fourth-order biharmonic equation. We design a cubic H³-nonconforming macro-element on two-dimensional triangular grids, solving a sixth-order tri-harmonic equation. We also write down explicitly the 12 basis functions on each macro-element. A convergence theory is established and verified by numerical tests.

Key words: Nonconforming macro-element, Minimum element, Tri-harmonic equation

中图分类号:

65N30
73C02

Jun Hu, Shangyou Zhang. A Cubic H³-Nonconforming Finite Element[J]. Communications on Applied Mathematics and Computation, 2019, 1(1): 81-100.

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A Cubic H³-Nonconforming Finite Element

A Cubic H³-Nonconforming Finite Element

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