TY - JOUR
T1 - Convergence of a Cell-Centered Finite Volume Method and Application to Elliptic Equations
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 536
EP - 566
PY - 2015
DA - 2015/12
SN - 12
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/501.html
KW - Finite Volume method, Taylor Series Expansion Scheme (TSES), convergence and stability, convex quadrilateral meshes.
AB - <p style="text-align: justify;">We study the consistency and convergence of the cell-centered Finite Volume (FV)
external approximation of $H^1_0(\Omega)$, where a 2D polygonal domain $\Omega$ is discretized by a mesh of
convex quadrilaterals. The discrete FV derivatives are defined by using the so-called Taylor Series
Expansion Scheme (TSES). By introducing the Finite Difference (FD) space associated with the
FV space, and comparing the FV and FD spaces, we prove the convergence of the FV external
approximation by using the consistency and convergence of the FD method. As an application,
we construct the discrete FV approximation of some typical elliptic equations, and show the
convergence of the discrete FV approximations to the exact solutions.</p>