强阻尼波动方程的非协调混合有限元分析

研究了非线性强阻尼波动方程的E_1~(Qrot)+Q_(10)×Q_(01)非协调混合有限元方法.利用该单元的高精度分析,借助于E_1~(Qrot)元所具有的两个性质:(a)其相容误差为O(h~2)阶比它的插值误差高一阶;(b)插值算子与Ritz投影等价,以及插值后处理技术,在半离散的格式下分别导出了原始变量u的H~1模和流量的L~2模下O(h~2)阶超逼近;整体超收敛性质.最后,通过构造一个新的全离散格式,得到了O(h~2+τ~2)的超逼近结果.

A Nonconforming Mixed Element Analysis for Nonlinear Strongly Damped Wave Equations

In this paper,with help of E_1~(Qrot)+Q_(10)×Q_(01)element,a nonconforming mixed finite element method for nonlinear strongly damped wave Equation is investigated By utilizing high accuracy analysis,two special properties of E_1~(Qrot)element:(a)the consistency error is of order O(h~2)which is one order higher than its interpolation error;(b)the interpolation operator is equivalent to its Ritz-projection operator,the super-close and the global super-convergence results with order O(h~2)for the primitive solution u in broken H~1-norm and flux variable  in L~2-norm are obtained through interpolated postprocessing approach,respectively for semi-discrete scheme.At the same time,the super-close results with order O(h~2+τ~2)are obtained through constructing a new full-discrete scheme.