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The mass-conserving domain decomposition method for convection diffusion equations with variable coefficients
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  • Ruiqi Dong,
  • Zhongguo Zhou,
  • Xiangdong Chen,
  • Huiguo Tang,
  • Qi Zhang
Ruiqi Dong
Shandong Agricultural University
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Zhongguo Zhou
Shandong Agricultural University
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Xiangdong Chen
Shandong Agricultural University
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Huiguo Tang
Shandong Agricultural University
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Qi Zhang
Shandong Agricultural University
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Abstract

In this paper, a conserved domain decomposition method for solving convection-diffusion equations with variable coefficients is analyzed. The interface fluxes over the sub-domains are firstly obtained by the explicit fluxes scheme. Secondly, the interior solutions and fluxes over each sub-domains are computed by the modified upwind implicit scheme. Then, the interface fluxes are corrected by the obtained solutions. We prove rigorously that our scheme is mass conservative, unconditionally stable and of second-order convergence in spatial step. Numerical examples test the theoretical analysis and efficiencies. Lastly, we extend our scheme to the nonlinear convection-diffusion equations and give the error estimate.

Peer review status:IN REVISION

19 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
21 Feb 2021Assigned to Editor
21 Feb 2021Submission Checks Completed
06 Mar 2021Reviewer(s) Assigned
12 Jun 2021Review(s) Completed, Editorial Evaluation Pending
13 Jun 2021Editorial Decision: Revise Minor