TY - JOUR
T1 - $H^1$-Stability and Convergence of the FE, FV and FD Methods for an Elliptic Equation
JO - East Asian Journal on Applied Mathematics
VL - 2
SP - 154
EP - 170
PY - 2018
DA - 2018/02
SN - 3
DO - http://doi.org/10.4208/eajam.030513.200513a 
UR - https://global-sci.org/intro/article_detail/eajam/10853.html
KW - Finite element method, finite difference method, finite volume method, Poisson equation, stability and convergence.
AB - <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>