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A posteriori error estimates for optimal control problems constrained by convection-diffusion equations
  • 时间：0
  • 分类：O241.82[理学—计算数学;理学—数学]
  • 作者机构：[1]中国工程物理研究院研究生院,北京100088, [2]山东师范大学数学科学学院,济南250014, [3]北京应用物理与计算数学研究所计算物理实验室,北京100088
  • 相关基金：国家自然科学基金（11571002,11471196,10971254,11301311）,中国工程物理研究院科学技术发展基金（2013A0202011,201580101021）和国防基础科研计划资助（B1520133015）.
作者： Hongfei FU[1], Hongxing RUI[2], Zhaojie ZHOU[3]
关键词： ANISOTROPIC, flow, model, ELLIPTIC, INTERFACE, problems, tensorcoefficients, immersed, INTERFACE, FINITE, ELEMENT, method, Crouzeix-Raviart, ELEMENT, anisotropic flow model, elliptic interface problems, tensor-coefficients, immersed interface finite element method, Crouzeix-Raviart element.
中文摘要：

<正>1引言多孔介质中含两种及以上不同传导性或渗透率的一些物理模型,都可以由间断系数为张量的二阶椭圆界面方程来刻画.为了服从守恒律,界面方程的解必须满足界面跳跃条件.当界面线充分光滑时,解在各个子区域上也分别都是光滑的.但因为扩散系数沿界面发生间断,解的整体正则性比较低,通常的数值方法难以得到理想的逼近精度.多种数值实验表明界面浸入有限元(IIFE)方法对于求解这类椭圆界面问题十分有效.这是由于这种方法把界面跳跃条件强加在有限元空间中,故不需要沿界面进行网格剖分.更多还原

英文摘要：

In this paper, an immersed Crouzeix-Raviart finite element method is developed for solving elliptic interface problems with discontinuous tensor- coefficients. The immersed interface finite element （IIFE） spaces are constructed by standard linear Crouzeix-Raviart-type polynomials on non-interface triangular elements and piecewise linear Crouzeix-Raviart-type polynomials on interface ele- ments, which both have edge averages as degrees of freedom. And the flux jump conditions are weakly enforced on the smooth interface. Numerical experiments are conducted to verify that the IIFE solutions possess optimal-order convergence in both the L2-norm and broken H1-norm.

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