拟线性黏弹性方程一个新的H^1-Galerkin混合有限元分析

New H^1-Galerkin mixed finite element analysis for quasi-linear viscoelasticity equation

利用不完全双二次元Q_2^-和一阶BDFM元,对拟线性黏弹性方程构造了一个新的H^1-Galerkin混合元模式。通过Bramble-Hilbert引理,证明了单元所对应的插值算子一个新的高精度结果。进一步地,在半离散和一个二阶全离散格式下,分别导出了原始变量u在H^1-模和中间变量珗p在H(div)-模意义下的超逼近性质。

A newH1-Galerkin mixed finite element pattern for quasi-linear viscoelasticity equation is constructed using incomplete biquadratic element Q2-and first order BDFM element. Through Bramble-Hilbert lemma,a newhigh precision results of interpolation operators corresponding to unit are proved. Further,the superclose properties for the primitive variables u in H1-norm and the intermediate variable p→ in H（ div）-norm are obtained respectively in semi-discrete and fully discrete schemes.