Speaker：Liuqiang Zhong (South China Normal University)

Time：2023-6-23, 11:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

First, an improved adaptive two-grid method with a correction step is designed, which is characterized in that before constructing a symmetric positive definite discrete scheme, an additional symmetric positive definite residual equation needs to be solved, and the residual is updated to the finite element solution of the upper level grid. Secondly, a new residual-based posterior error indicator is constructed, and further by the reliability of the error indicator, the quasi-orthogonality of the energy norm error and the decaying property of the global posterior error indicator, we obtain the convergence of the improved adaptive two-grid method. Finally, corresponding numerical experiments are given to verify the effectiveness of the improved adaptive two-grid method. Compared with the existing adaptive two-grid method, experiments show that in some cases, for the same degree of freedom, the improved adaptive two-grid method has higher error accuracy, and is more robust to the coefficients of the model problem and the adaptive approach for the parameters.