Year: 2017
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 879–892
Abstract
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 $\rightarrow$ Mark $\rightarrow$ Refine. The novelty of our method is that we do not have the traditional "completion" 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2017-IJNAM-10485
International Journal of Numerical Analysis and Modeling, Vol. 14 (2017), Iss. 6 : pp. 879–892
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Adaptive finite volume method hanging nodes hybrid meshes error analysis.