no. 2
A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 2, pp. 385-406

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 L 2 -norm is proved. By duality argument and Oswald interpolation, a posteriori error estimates for the errors in L 2 -norm and W 1 , p -seminorm are also obtained. Finally, numerical examples are provided to validate the theoretical analysis.

DOI : 10.1051/m2an/2022005
Classification : 49M25, 65K10, 65M50
Keywords: Hybridizable discontinuous Galerkin method, a priori error estimate, a posteriori error estimate, elliptic equation, Dirac measure 
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     author = {Leng, Haitao and Chen, Yanping},
     title = {A hybridizable discontinuous {Galerkin} method for second order elliptic equations with {Dirac} delta source},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {385--406},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {2},
     doi = {10.1051/m2an/2022005},
     mrnumber = {4379608},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/m2an/2022005/}
}
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Leng, Haitao; Chen, Yanping. A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 2, pp. 385-406. doi: 10.1051/m2an/2022005

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