A Recovery Based Linear Finite Element Method For 1D Bi-Harmonic Problems
A Recovery Based Linear Finite Element Method For 1D Bi-Harmonic Problems
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DOI：
10.1007/s10915-015-0141-1
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发表时间：
2016-07
影响因子：
2.5
通讯作者：
Hongtao Chen;Zhimin Zhang;Q. Zou
中科院分区：
文献类型：
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作者：
Hongtao Chen;Zhimin Zhang;Q. Zou
分析了求解双调和方程及其特征值问题的基于梯度恢复的线性有限元方法。该方法只使用一个单元，避免了复杂的单元构造和重复单元构造。在不同的Sobolev范数下建立了最优误差界。此外，经过后处理的恢复梯度是超收敛到确切的。数值实验验证了我们的理论结果。作为应用，本文还将新方法用于数值求解一维完全非线性Monge-Ampère方程。
We analyze a gradient recovery based linear finite element method to solve bi-harmonic equations and the corresponding eigenvalue problems. Our method uses onlyelement, which avoids complicated construction ofelements and nonconforming elements. Optimal error bounds under various Sobolev norms are established. Moreover, after a post-processing the recovered gradient is superconvergent to the exact one. Some numerical experiments are presented to validate our theoretical findings. As an application, the new method has been also used to solve 1-D fully nonlinear Monge–Ampère equation numerically.