【作者】 董晓靖；

【导师】 石东洋；

【作者基本信息】 郑州大学 ， 计算数学， 2012， 硕士

【摘要】 本论文包括两部分.第一部分主要研究发展型非线性对流扩散方程的双线性元及非协调EQ1rot元逼近,给出了L2(Ω)模意义下的最优ε一致收敛性结果.同时根据Bramble-Hilbert引理分别导出了高精度的积分恒等式,并由此导出了一些新的渐近展开式.利用外推技巧得到了具有三阶精度的近似解.第二部分主要研究了强阻尼波动方程的H1-Galerkin混合有限元方法的超收敛性.借助于协调线性三角形元已有的分析估计式,直接利用插值算子代替原始变量μ的Ritz投影和应力变量p的Ritz-Volterra投影.对半离散和全离散格式,得到了μ在H1(Ω)模和p在H(div;Ω)模意义下比以往文献高一阶的超逼近和超收敛结果.更多还原

【Abstract】 This dissertation mainly includes two parts. In the first part, the optimal ε uniform convergent results of bilinear conforming finite element and nonconforming finite element EQ1rot are obtained under L2(Ω) norm for the time-dependent nonlinear advection-diffusion equations. Based on Bramble-Hilbert lemma, higher accuracy integral identities and some new asymptotic expansions are derived. Moreover, we derive the related approximate solutions with third order by use of the extrapolation technique. In the second part, the superconvergence analysis of H1-Galerkin mixed finite element method for strongly damped wave equations is studied. By virtue of the interpolation technique operator instead of Ritz projection of the original variable u and Ritz-Volterra projection of the stress variable p, the superclose and superconvergence results in in(Q) norm for u and H (div;Ω) norm for p for both semidiscrete and fully discrete schemes are derived through applying some error estimates of conforming linear triangular finite element.更多还原