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

被引：0
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作者：
Hongtao Chen
Xiaobing Feng
Zhimin Zhang
机构：
[1] Xiamen University,School of Mathematical Sciences
[2] Xiamen University,Fujian Provincial Key Laboratory of Mathematical Modeling and High
[3] The University of Tennessee,Performance Scientific Computing
[4] Beijing Computational Science Research Center,Department of Mathematics
[5] Wayne State University,Department of Mathematics
来源：
Advances in Computational Mathematics | 2021年 / 47卷
关键词：
Monge-Ampère equation; Vanishing moment method; Gradient recovery; Linear finite element; 65N30; 35J60;
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摘要：
This paper develops a new recovery-based linear C0 finite element method for approximating the weak solution of a fourth-order singularly perturbed Monge-Ampère equation, which is known as the vanishing moment approximation of the Monge-Ampère equation. The proposed method uses a gradient recovery technique to define a discrete Laplacian for a given linear C0 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 C0 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 C0 finite element method.
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