Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods
Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods
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DOI：
10.1016/j.apnum.2019.09.010
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发表时间：
2020-04
影响因子：
2.8
通讯作者：
Woocheol Choi;Sanghyu Lee
中科院分区：
文献类型：
--
作者：
Woocheol Choi;Sanghyu Lee
本文利用间断的增广Galerkin有限元方法，给出了Dirac源远离奇点的椭圆问题的最优先验误差估计。在均匀网格上，具有Dirac源项的椭圆型问题的有限元解是次优收敛的。然而，在这里，我们采用归纳估计和L2范数，以获得最佳的顺序，排除小球区域的奇异性的二维和三维域。数值例子证实了我们的理论结果。
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 L 2 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.