Regularity and Finite Element Approximation for Two-Dimensional Elliptic Equations with Line Dirac Sources
Regularity and Finite Element Approximation for Two-Dimensional Elliptic Equations with Line Dirac Sources
复制标题
线性狄拉克源二维椭圆方程的正则性和有限元逼近
DOI：
10.1016/j.cam.2021.113518
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发表时间：
2021
影响因子：
2.4
通讯作者：
Zhao, Lewei.
中科院分区：
文献类型：
--
作者：
Li, Hengguang;Wan, Xiang;Yin, Peimeng;Zhao, Lewei.
研究了二维区域中以线Dirac δ函数为源项的椭圆型方程的Dirichlet边界条件。这样的线狄拉克测度导致不同类型的解决方案在附近的线断裂的奇异性。我们建立了一类加权Sobolev空间中的解的新的正则性结果，并提出了以最优收敛速度逼近奇异解的有限元算法。数值试验证明理论研究结果。
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the neighborhood of the line fracture. We establish new regularity results for the solution in a class of weighted Sobolev spaces and propose finite element algorithms that approximate the singular solution at the optimal convergence rate. Numerical tests are presented to justify the theoretical findings.