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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.
}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/10485.html} }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.