Volume 56, Number 2, March-April 2022
|Page(s)||385 - 406|
|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: firstname.lastname@example.org
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
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