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arXiv · 2012.12370

Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources

Hengguang Li·Xiang Wan·Peimeng Yin·Lewei Zhao
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Abstract

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.

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Hengguang Li, Xiang Wan, Peimeng Yin, Lewei Zhao. 2020-12-22. Regularity and finite element approximation for two-dimensional elliptic equations with line Dirac sources. https://doi.org/10.1016/j.cam.2021.113518

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