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Convergence analysis of new additive Schwarz method for solving nonselfadjoint elliptic problems
Fenfen Qi,Shishun Li,Xinping Shao
Keywords:Additive Schwarz method, AHSS iteration, Nonselfadjoint elliptic problems, Convergence rate
      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 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-dominated convection-diffusion equations.