Sine-Gordon方程H^1-Galerkin非协调混合有限元法的误差分析  

Error Analysis of An H^1-Galerkin Nonconforming Mixed Finite Element Method for Sine-gordon Equations

作　　者：史艳华[1] 王萍莉[1] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000

出　　处：《许昌学院学报》2015年第5期1-6,共6页Journal of Xuchang University

基　　金：许昌市科技局项目(1504002);许昌学院青年骨干教师项目

摘　　要：讨论非线性Sine-Gordon方程H1-Galerkin非协调混合元方法的半离散和全离散逼近格式.利用非协调EQrot1元空间逼近标量空间、利用交叉单元空间逼近向量空间.借助这两个单元的性质及插值理论,分别得到了两种格式下原始变量和流量在H1模和H(div,Ω)模下具有O(h)/O(h+τ2)阶的最优误差估计式.In this paper, an H^1-Galerkin nonconforming mixed finite element method is mainly proposed for Sine-Gordon equations under semi-discrete and fully-discrete schemes. The space of nonconforming EQ1^rot element is taken to approximate scalar space, and the interaction finite element to approximate vector space. By use of the properties of the elements and interpolation theory, the optimal order error estimates are derived for the original variable in borken H^1 norm and the flux variable in H（div,Ω） norm with order O（h）/O（h ＋ τ^2） for two schemes, respectively.

关 键 词：SINE-GORDON方程 H^1-Galerkin混合元方法 半离散和全离散 误差估计 

分 类 号：O242.21[理学—计算数学]