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 AM  Vol.9 No.6 , June 2018
Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems
Anna Harris1*, Stephen Harris2, Camille Gardner1, Tyrone Brock1
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Abstract:
The superconvergence in the finite element method is a phenomenon in which the finite 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. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
Keywords: Conforming Finite Element Methods, Superconvergence, L2-Projection, Second Order Elliptic Equationm, MATLAB
Cite this paper: Harris, A. , Harris, S. , Gardner, C. and Brock, T. (2018) Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems. Applied Mathematics, 9, 691-701. doi: 10.4236/am.2018.96047.
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