A Posteriori Error Estimation for a New Stabilized Discontinuous Galerkin Method

2002 ◽  
Author(s):  
A. Romkes ◽  
S. Prudhomme ◽  
J. T. Oden
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Error Estimation ◽  
Discontinuous Galerkin Method ◽  
Posteriori Error ◽  
A Posteriori Error Estimation ◽  
A Posteriori ◽  
Posteriori Error Estimation ◽  
A Posteriori Error

scholarly journals ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS

2007 ◽  
Vol 17 (01) ◽  
pp. 33-62 ◽  
Author(s):  
PAUL HOUSTON ◽  
DOMINIK SCHÖTZAU ◽  
THOMAS P. WIHLER
Keyword(s):  
Discontinuous Galerkin ◽  
Error Estimation ◽  
Elliptic Boundary ◽  
Posteriori Error ◽  
A Posteriori Error Estimation ◽  
Energy Norm ◽  
Upper And Lower Bounds ◽  
A Posteriori ◽  
Posteriori Error Estimation ◽  
A Posteriori Error

In this paper, we develop the a posteriori error estimation of hp-version interior penalty discontinuous Galerkin discretizations of elliptic boundary-value problems. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The bounds are explicit in the local mesh sizes and approximation orders. A series of numerical experiments illustrate the performance of the proposed estimators within an automatic hp-adaptive refinement procedure.

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