scholarly journals Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs

2016 ◽  
Vol 85 (301) ◽  
pp. 2099-2129 ◽  
Author(s):  
Alexandre Ern ◽  
Friedhelm Schieweck
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Stabilized Finite Element ◽  
First Order ◽  
Stabilized Finite Element Method ◽  
Element Method

Convergence and Quasi-Optimality of an Adaptive Multi-Penalty Discontinuous Galerkin Method

2016 ◽  
Vol 9 (1) ◽  
pp. 51-86
Author(s):  
Zhenhua Zhou ◽  
Haijun Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Diffusion Problem ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Interior Penalty ◽  
Element Method

AbstractAn adaptive multi-penalty discontinuous Galerkin method (AMPDG) for the diffusion problem is considered. Convergence and quasi-optimality of the AMPDG are proved. Compared with the analyses for the adaptive finite element method or the adaptive interior penalty discontinuous Galerkin method, extra works are done to overcome the difficulties caused by the additional penalty terms.

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