伪双曲方程非协调H~1-Galerkin有限元超逼近分析

针对一类伪双曲方程,建立了其非协调H~1-Galerkin混合有限元逼近格式利用非协调带约束旋转(CNR)Q_1及零阶Raviart-Thomas(R-T)元作为逼近空间对,并借助他们的特殊性质,在半离散格式下得到了原始变量u的broken-H~1模以及流量p=▽u的H(div,Ω)模的O(h~2)阶超逼近估计.同时,构造了一个具有二阶精度的全离散格式,并得到了相关变量的O(h~2+τ~2)阶超逼近结果.最后,给出了数值算例验证理论分析的正确性.

An H~1-Galerkin Nonconforming Mixed Finite Element Method for Pseudo-Hyperbolic Equations

An H~1-Galerkin nonconforming mixed finite element method( MFEM) is proposed to analyze a class of pseudo-hyperbolic equations. Taking of the constrained nonconforming rotated( CNR) Q_1 element and the zero order Raviart-Thomas( R-T) element as the approximation element pair and using of the typical characters of these elements,the super-close estimates of order O( h~2) of original variable u in broken-H~1 norm and flux variable p= ▽u in H( div,Ω) norm for semi-discrete scheme are derived. Then,we construct the two order fully-discrete scheme and obtain the super-close estimates of order O( h~2+ τ~2) for the relevant variables. Finally,we carry out a numerical example to confirm the theoretical analysis.