CONVERGENCE ANALYSIS OF NEW ADDITIVE SCHWARZ METHOD FOR SOLVING NONSELFADJOINT ELLIPTIC PROBLEMS

Fenfen Qi; Shishun Li; Xinping Shao

doi:10.11948/20190256

2021 Volume 11 Issue 1

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Fenfen Qi, Shishun Li, Xinping Shao. CONVERGENCE ANALYSIS OF NEW ADDITIVE SCHWARZ METHOD FOR SOLVING NONSELFADJOINT ELLIPTIC PROBLEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 192-209. doi: 10.11948/20190256

Citation:

Fenfen Qi, Shishun Li, Xinping Shao. CONVERGENCE ANALYSIS OF NEW ADDITIVE SCHWARZ METHOD FOR SOLVING NONSELFADJOINT ELLIPTIC PROBLEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 192-209. doi: 10.11948/20190256

CONVERGENCE ANALYSIS OF NEW ADDITIVE SCHWARZ METHOD FOR SOLVING NONSELFADJOINT ELLIPTIC PROBLEMS

1.
School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454003, China
2.
School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

Corresponding author: Email address: lss6@sina.com(S. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (Nos. 11726636, 11701133), Natural Science Foundation of Henan(No. 212300410347) and Fundamental Research Funds for the Universities of Henan Province (No. NSFRF200315)

Abstract

Abstract

In this paper, we present a two-level additive Schwarz method for solving a system arising from the discretization of the nonselfadjoint elliptic equation. By employing the Cauchy-Schwarz-type inequality and stable decomposition under the energy norm, we obtain the optimal convergence theory for the proposed method. It shows that the convergence rate is bounded and independent of the fine mesh size and the number of subdomains. Some numerical results are reported to verify our theoretical result. Moreover, we demonstrate the benefit compared to the classical two-level additive Schwarz algorithm for solving convection-diffusion equations.
- Additive Schwarz method /
- AHSS iteration /
- nonselfadjoint elliptic problems /
- convergence rate
MSC: 65N55, 65N30

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References

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