Two-level preconditioning of discontinuous Galerkin approximations of second-order elliptic equations

2006 ◽  
Vol 13 (9) ◽  
pp. 753-770 ◽  
Author(s):  
Veselin A. Dobrev ◽  
Raytcho D. Lazarov ◽  
Panayot S. Vassilevski ◽  
Ludmil T. Zikatanov
Keyword(s):  
Discontinuous Galerkin ◽  
Elliptic Equations ◽  
Second Order ◽  
Galerkin Approximations ◽  
Second Order Elliptic Equations

scholarly journals A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source

2022 ◽  
Author(s):  
Haitao Leng ◽  
Yanping Chen
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Elliptic Equations ◽  
A Posteriori Error Estimates ◽  
Second Order ◽  
Dirac Delta ◽  
Hybridizable Discontinuous Galerkin ◽  
Hybridizable Discontinuous Galerkin Method ◽  
Second Order Elliptic Equations

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.

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