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A Mortar Mixed Finite Volume Method for Elliptic Problems on Non-matching Multi-block Triangular Grids

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Abstract

A mixed finite volume method is considered for the mixed formulation of second-order elliptic equations. The computational domain can be decomposed into non-overlapping sub-domains or blocks and the diffusion tensors may be discontinuous across the sub-domain boundaries. We define a conforming triangular partition on each sub-domain independently, and employ the standard mixed finite volume method within each sub-domain. A mortar finite element space is introduced to approximate the trace of the pressure on the non-matching interfaces. Moreover, a continuity condition of flux is imposed weakly. We prove the scheme’s first order optimal rate of convergence for both the pressure and the velocity. Numerical experiments are provided to illustrate the error behavior of the scheme and confirm our theoretical results.

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Acknowledgements

We appreciate the anonymous referees for their constructive comments on improving this paper.

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Authors and Affiliations

  1. College of Mathematics, Jilin University, Changchun, 130012, Jilin, People’s Republic of China

    Yanni Gao & Yonghai Li

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  1. Yanni Gao
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  2. Yonghai Li
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Correspondence to Yonghai Li.

Additional information

This work is partially supported by the National Natural Science Foundation of China under Grant Number 11371170, the NASF under Grant Number U1630249 and the Science Challenge Program under Number JCKY2016212A502.

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Gao, Y., Li, Y. A Mortar Mixed Finite Volume Method for Elliptic Problems on Non-matching Multi-block Triangular Grids. J Sci Comput 73, 50–69 (2017). https://doi.org/10.1007/s10915-017-0405-z

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  • DOI: https://doi.org/10.1007/s10915-017-0405-z

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