Abstract

A new time discretization method for strongly nonlinear parabolic systems is con- structed by combining the fully explicit two-step backward difference formula and a second-order stabilization of wave type. The proposed method linearizes and decouples a nonlinear parabolic system at every time level, with second-order consistency error. The convergence of the proposed method is proved by combining energy estimates for evolution equations of parabolic and wave types with the generating function technique that is popular in studying ordinary differential equations. Several numerical examples are provided to support the theoretical result.

Short bio

周冠宇，本科毕业于南开大，2015年在东京大学获得博士学位，2015年至2017年在同大学任博士后，2017年月至2019年在东京理科大学应用数学系任助理教授，2019年至今在电子科技大学任教授。主要从事偏微分方程数值方法和数学物理方程的研究，研究课题有非典型边界条件的流体方程的有限元方法和DG法，趋化性方程的有限体积法等，主要研究成果在SIAM Numer. Anal., Numer. Math., J. Sci. Comput.等计算数学和偏微分方程等学术刊物上发表。