| Issue |
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
|
|
|---|---|---|
| Page(s) | 385 - 406 | |
| DOI | https://doi.org/10.1051/m2an/2022005 | |
| Published online | 14 February 2022 | |
A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, Guangdong, P.R. China
* Corresponding author: yanpingchen@scnu.edu.cn
Received:
2
November
2020
Accepted:
11
January
2022
In this paper, we investigate a hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac measures. Under assumption that the domain is convex and the mesh is quasi-uniform, a priori error estimate for the error in L2-norm is proved. By duality argument and Oswald interpolation, a posteriori error estimates for the errors in L2-norm and W1,p-seminorm are also obtained. Finally, numerical examples are provided to validate the theoretical analysis.
Mathematics Subject Classification: 49M25 / 65K10 / 65M50
Key words: Hybridizable discontinuous Galerkin method / a priori error estimate / a posteriori error estimate / elliptic equation / Dirac measure
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.