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The finite volume method for two-dimensional Burgers’ equation

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Abstract

The Burgers’ equation as a useful mathematical model is applied in many fields such as fluid dynamic, heat conduction, and continuous stochastic processes. Although this equation can be solved analytically, it is only based on the restricted set of initial-boundary value conditions. So the numerical method for solving the Burgers’ equation is necessary. In this paper, a finite volume method is presented for the two-dimensional Burgers’ equation on a triangular mesh. We give a semi-discrete finite volume scheme and drive the optimal error estimate in H1 norm.

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Funding

This work was supported by the National Natural Science Foundation of China (71671033, 71371190, 11371081) and Fundamental Research Funds for the Central Universities (N160601001).

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Northeastern University, Shenyang, China

    Ying Sheng & Tie Zhang

Authors
  1. Ying Sheng
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  2. Tie Zhang
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Correspondence to Ying Sheng.

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Sheng, Y., Zhang, T. The finite volume method for two-dimensional Burgers’ equation. Pers Ubiquit Comput 22, 1133–1139 (2018). https://doi.org/10.1007/s00779-018-1143-4

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  • DOI: https://doi.org/10.1007/s00779-018-1143-4

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