期刊论文

Error Estimates for Expanded Mixed Finite Element Methods for Nonlinear Hyperbolic Equation

中文

数学物理学报

1003-3998

2021

41

02

468-478

10.3969/j.issn.1003-3998.2021.02.016

湖南省重点实验室项目基金（2016TP1020）； 衡阳师范学院科学基金（18D12）~~；

本校为第一机构

该文针对一类非线性双曲型方程提出了扩展混合有限元方法.首先,建立了半离散扩展混合元格式,获得了半离散扩展混合元解的${L^\infty }\left( {{L^2}} \right)$先验误差估计.然后,利用有限差分法对时间项进行离散,建立了全离散扩展混合元格式,并给出了全离散格式下的先验误差估计.最后,通过数值算例验证了理论结果.

In this paper, expanded mixed finite element method is developed for a class of nonlinear hyperbolic equation. A priori error estimate for the space discrete scheme is discussed in ${L^\infty }\left( {{L^2}} \right)$ norm. Centered finite differences are used to advance in time, a fully discrete scheme is proposed. Further, a priori error estimate for the fully discrete scheme is established. Finally, a numerical exampl...