一类非线性双曲型方程扩展混合有限元方法的误差估计  

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

作　　者：王克彦 王奇生[2] Wang Keyan;Wang Qisheng(School of Mathematics and Statistics,Hengyang Normal University,Hunan Hengyang 421008;School of Mathematics and Computational Science,Wuyi University,Guangdong Jiangmen 529020)

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421008 [2]五邑大学数学与计算科学学院,广东江门529020

出　　处：《数学物理学报（A辑）》2021年第2期468-478,共11页Acta Mathematica Scientia

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

摘　　要：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^(∞)(L^(2))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^(∞)(L^(2))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 example is presented to confirm the theoretical results.

关 键 词：非线性双曲型方程 扩展混合有限元方法 误差估计 

分 类 号：O241.82[理学—计算数学]