TITLE:
Numerical Experiments Using MATLAB: Superconvergence of Conforming Finite, Element Approximation for Second Order, Elliptic Problems
AUTHORS:
Anna Harris, Stephen Harris, Camille Gardner, Tyrone Brock
KEYWORDS:
Conforming Finite Element Methods, Superconvergence, L2-Projection, Second Order Elliptic Equationm, MATLAB
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.6,
June
29,
2018
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.