ADAPTIVE MESH REFINEMENT FOR ELLIPTIC INTERFACE PROBLEMS USING THE NON-CONFORMING IMMERSED FINITE ELEMENT METHOD
ADAPTIVE MESH REFINEMENT FOR ELLIPTIC INTERFACE PROBLEMS USING THE NON-CONFORMING IMMERSED FINITE ELEMENT METHOD
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发表时间：
2011
影响因子：
1.1
通讯作者：
Chin-Tien Wu;Zhilin Li;M. Lai
中科院分区：
文献类型：
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作者：
Chin-Tien Wu;Zhilin Li;M. Lai
本文针对文献[25]中提出的非协调浸入式有限元（IFE）方法，提出并分析了一种自适应网格加密技术。发展了求解二阶椭圆边值问题的IFE方法，该问题的边界系数可能是间断的。IFE方法基于不需要拟合界面的三角测量。IFE方法的核心思想之一是修改基函数，使其满足跨界面的自然跳跃条件。IFE方法在L2范数和H1范数下分别为O（h2）和O（h）阶。为了发展自适应网格加密技术，本文推导了附加的先验和后验误差估计。我们的新的先验误差估计表明，通用常数仅与扩散系数β−和β+之比成线性比例，这改进了[25]中的相应结果。* 通讯作者。国立交通大学应用数学系，新竹市大学路1001号。ctw@math.nctu.edu.tw北卡罗来纳州州立大学，罗利，科学计算研究中心和数学系。27695-8205.国立交通大学数学模拟与科学计算中心，新竹市大学路1001号，邮编300。
In this paper, an adaptive mesh refinement technique is developted and analyzed for the non-conforming immersed finite element (IFE) method proposed in [25]. The IFE method was developed for solving the second order elliptic boundary value problem with interfaces across which the coefficient may be discontinuous. The IFE method was based on a triangulation that does not need to fit the interface. One of the key ideas of IFE method is to modify the basis functions so that the natural jump conditions are satisfied across the interface. The IFE method has shown to be order of O(h2) and O(h) in L2 norm and H1 norm, respectively. In order to develop the adaptive mesh refinement technique, additional priori and posterior error estimations are derived in this paper. Our new a priori error estimation shows that the generic constant is only linearly proportional to ratio of the diffusive coefficients β− and β+, which improves the corresponding result in [25]. ∗Corresponding author. Department of Applied Mathematics, National Chiao-Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan. ctw@math.nctu.edu.tw †Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC. 27695-8205. ‡Center of mathematical modeling and Scientific computing, National Chiao-Tung University, 1001, Ta Hsueh Road, Hsinchu 300, Taiwan.