@Article{EAJAM-3-154,
author = {Yinnian He and Xinlong Feng},
title = {$H^1$-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation},
journal = {East Asian Journal on Applied Mathematics},
year = {2018},
volume = {3},
number = {2},
pages = {154--170},
abstract = {<p style="text-align: justify;">We obtain the coefficient matrices of the finite element (FE), finite volume
(FV) and finite difference (FD) methods based on $P_1$-conforming elements on a quasi-uniform
mesh, in order to approximately solve a boundary value problem involving the
elliptic Poisson equation. The three methods are shown to possess the same $H^1$-stability
and convergence. Some numerical tests are made, to compare the numerical results
from the three methods and to review our theoretical results.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.030513.200513a },
url = {http://global-sci.org/intro/article_detail/eajam/10853.html}
}