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

Yanhui Zhou and Qingsong Zou

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

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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 → Estimate → Mark → 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.

  • History

Published online: 2017-10

  • AMS Subject Headings

35R35, 49J40, 60G40.

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