A recovery-based linear C0 finite element method for a fourth-order singularly perturbed Monge-Ampere equation

被引：5
|
作者：
Chen, Hongtao [1 ,2 ]
Feng, Xiaobing [3 ]
Zhang, Zhimin [4 ,5 ]
机构：
[1] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
[2] Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Peoples R China
[3] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA
[4] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China
[5] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2021年 / 47卷 / 02期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Monge-Ampere equation; Vanishing moment method; Gradient recovery; Linear finite element; 65N30; 35J60;
D O I：
10.1007/s10444-021-09847-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper develops a new recovery-based linear C-0 finite element method for approximating the weak solution of a fourth-order singularly perturbed Monge-Ampere equation, which is known as the vanishing moment approximation of the Monge-Ampere equation. The proposed method uses a gradient recovery technique to define a discrete Laplacian for a given linear C-0 finite element function (offline), the discrete Laplacian is then employed to discretize the biharmonic operator appeared in the equation. It is proved that the proposed C-0 linear finite element method has a unique solution using a fixed point argument and the corresponding error estimates are derived in various norms. Numerical experiments are also provided to verify the theoretical error estimates and to demonstrate the efficiency of the proposed recovery-based linear C-0 finite element method.
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页数：37
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