电报方程的一个最低阶新混合元格式逼近

A new lowest order mixed finite element scheme approximation for telegraph equations

针对电报方程构造一个新的最低阶三角形协调混合元格式,证明了该格式解的存在唯一性.在抛弃传统有限元分析中不可或缺的Ritz投影的情况下,利用积分恒等式和平均值技巧,在半离散情形下分别导出了原始变量在H1模及流量在L2模意义下的超逼近性质.借助新构造的插值后处理算子,得到了相应的整体超收敛结果.

A new lowest order triangular conforming mixed finite element formulation was proposed for telegraph equations,and the existence and uniqueness of the above pattern were proved.With the help of the integral identity and mean-value technique,the superclose properties for the primitive solution in H1-norm and the flux in L2-norm for semi-discrete scheme were obtained without requiring the Ritz projection operator which was indispensable in traditional finite element analysis,respectively.Furthermore,by employing a new constructed interpolated postprocessing approach,the corresponding superconvergence results were deduced.