@article{ChoiLee_2019,
title = "Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods",
journal = "Applied Numerical Mathematics",
volume = "150",
pages = "76 - 104",
year = "2020",
issn = "0168-9274",
doi = "https://doi.org/10.1016/j.apnum.2019.09.010",
url = "http://www.sciencedirect.com/science/article/pii/S0168927419302491",
author = "Woocheol Choi and Sanghyun Lee",
keywords = "Singularity, Dirac source, Discontinuous Galerkin finite element methods, Enriched Galerkin finite element methods, A priori estimates",
abstract = "We present an optimal a priori error estimates of the elliptic problems with Dirac sources away from the singular point using discontinuous and enriched Galerkin finite element methods. It is widely shown that the finite element solutions for elliptic problems with Dirac source terms converge sub-optimally in classical norms on uniform meshes. However, here we employ inductive estimates and L2 norm to obtain the optimal order by excluding the small ball regions with the singularities for both two and three dimensional domains. Numerical examples are presented to substantiate our theoretical results."
}

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