scholarly journals Interior Penalty Discontinuous Galerkin Methods for Second Order Linear Non-divergence Form Elliptic PDEs

2017 ◽  
Vol 74 (3) ◽  
pp. 1651-1676 ◽  
Author(s):  
Xiaobing Feng ◽  
Michael Neilan ◽  
Stefan Schnake
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Divergence Form ◽  
Second Order ◽  
Elliptic Pdes ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Order Linear

Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

2020 ◽  
Vol 28 (3) ◽  
pp. 161-174
Author(s):  
Maurice S. Fabien ◽  
Matthew G. Knepley ◽  
Beatrice M. Riviere
Keyword(s):  
Error Estimates ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Computational Cost ◽  
Elliptic Problems ◽  
Second Order ◽  
Three Dimensions ◽  
Galerkin Methods ◽  
Interior Penalty ◽  
Second Order Elliptic Problems

AbstractThe focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L2-norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.

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