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High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems

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Abstract

Based on the combination of block-centered and compact difference methods, fourth order compact block-centered finite difference schemes for the numerical solutions of one-dimensional and two-dimensional elliptic and parabolic problems with variable coefficients are derived and analyzed. Stability and optimal fourth-order error estimates are proved for both the solution and flux. Numerical experiments for model problems are presented to confirm the theoretical results and superior performance of the proposed schemes.

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Authors and Affiliations

  1. School of Mathematical Sciences, Ocean University of China, Qingdao, 266100, People’s Republic of China

    Yilei Shi, Shusen Xie & Kai Fu

  2. Department of Mathematics and Statistics, York University, Toronto, ON, M3J 1P3, Canada

    Dong Liang

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  1. Yilei Shi
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  2. Shusen Xie
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  3. Dong Liang
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  4. Kai Fu
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Correspondence to Shusen Xie.

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The second author (Xie) was partially supported by National Natural Science Foundation of China Grants 11871443. The third author (Liang) was partially supported by Natural Sciences and Engineering Research Council of Canada. The fourth author (Fu) was partially supported by National Natural Science Foundation of China Grants 11601497.

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Shi, Y., Xie, S., Liang, D. et al. High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems. J Sci Comput 87, 86 (2021). https://doi.org/10.1007/s10915-021-01507-x

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  • DOI: https://doi.org/10.1007/s10915-021-01507-x

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