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Volume 14, Issue 6
A Novel Adaptive Finite Volume Method for Elliptic Equations

Yanhui Zhou & Qingsong Zou

Int. J. Numer. Anal. Mod., 14 (2017), pp. 879-892.

Published online: 2017-10

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  • 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.

  • Keywords

Adaptive finite volume method, hanging nodes, hybrid meshes, error analysis.

  • AMS Subject Headings

35R35, 49J40, 60G40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-879, author = {Yanhui Zhou and Qingsong Zou}, title = {A Novel Adaptive Finite Volume Method for Elliptic Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2017}, volume = {14}, number = {6}, pages = {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.

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

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.

Yanhui Zhou and Qingsong Zou. (2017). A Novel Adaptive Finite Volume Method for Elliptic Equations. International Journal of Numerical Analysis and Modeling. 14 (6). 879-892. doi:
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