TITLE:
Numerical Experiments Using MATLAB: Superconvergence of Nonconforming Finite Element Approximation for Second-Order Elliptic Problems
AUTHORS:
Anna Harris, Stephen Harris, Danielle Rauls
KEYWORDS:
Nonconforming Finite Element Methods, Superconvergence, L2-Projection, Second-Order Elliptic Equation
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.17,
November
22,
2016
ABSTRACT: 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://github.com/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.