论文标题
二维椭圆方程的规律性和有限元近似，带有线dirac源
Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources
论文作者
论文摘要
我们研究具有二维域中dirichlet边界条件的源术语的椭圆方程。这样的线dirac测量导致线断裂附近的不同类型的溶液奇异性。我们在一类加权Sobolev空间中为解决方案建立了新的规律性结果，并提出了有限元算法，该算法以最佳收敛速率近似于单数溶液。提出了数值测试以证明理论发现是合理的。
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.
