TY - JOUR
T1 - A Novel Adaptive Finite Volume Method for Elliptic Equations
AU - Yanhui Zhou & Qingsong Zou
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 879
EP - 892
PY - 2017
DA - 2017/10
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10485.html
KW - Adaptive finite volume method, hanging nodes, hybrid meshes, error analysis.
AB - <p style="text-align: justify;">In this paper, we propose a novel adaptive finite volume method (AFVM) for elliptic
equations. As a standard adaptive method, a loop of our method involves four steps: Solve $\rightarrow$ Estimate <span style="text-align: justify;">$\rightarrow$</span> Mark <span style="text-align: justify;">$\rightarrow$</span> Refine. The novelty of our method is that we do not have the traditional
&quot;completion&quot; procedure in the Refine step. To guarantee the conformity, a triangular element with
a hanging node is treated as a quadrilateral element, and the corresponding function space consists
of the bilinear functions. The optimal computational complexity of our AFVM is validated by
numerical examples.</p>