Speaker: Yi Lijun, professor and doctoral supervisor, Shanghai Normal University

Date: December 7, 2024

Time: 10:00-12:00 am

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

We propose a unified postprocessing technique for Galerkin methods (including CG and DG) applied to solve initial value problems for first and second-order ODEs. The core idea of this postprocessing technique is to augment the existing Galerkin approximation of degree k with an additional term involving a generalized Jacobi polynomial (multiplied by appropriate coefficients) of degree k+1. The theoretical findings suggest that, through postprocessing, the convergence rate of the original Galerkin approximation error can be elevated by one order. As an application, we extend this postprocessing technique to the Galerkin time discretization of nonlinear parabolic and hyperbolic equations in the temporal direction. Abundant numerical results underscore the effectiveness and high accuracy of the proposed postprocessing technique.

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https://view.sdu.edu.cn/info/1020/197542.htm