Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for Second-Order Elliptic Problems
Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for Second-Order Elliptic Problems作者机构：Department of Mathematics and Computer Science University of Arkansas at Pine Bluff Pine Bluff Arkansas USA US Food and Drug Administration National Center for Toxicology Research Jefferson Arkansas USA
出 版 物：《Applied Mathematics》 (应用数学（英文）)
年 卷 期：2016年第7卷第17期
页 面：2174-2182页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Nonconforming Finite Element Methods Superconvergence L2-Projection Second-Order Elliptic Equation
摘 要：The superconvergence in the finite element method is a phenomenon in which the fi-nite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. However, since the conforming finite element method (CFEM) requires a strong continuity, it is not easy to construct such finite elements for the complex partial differential equations. Thus, the nonconforming finite element method (NCFEM) is more appealing computationally due to better stability and flexibility properties compared to CFEM. The objective of this paper is to establish a general superconvergence result for the nonconforming finite element approximations for second-order elliptic problems by L2-projection methods by applying the idea presented in Wang. MATLAB codes are published at https://***/annaleeharris/Superconvergence-NCFEM for anyone to use and to study. The results of numerical experiments show great promise for the robustness, reliability, flexibility and accuracy of superconvergence in NCFEM by L2- projections.
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