scholarly journals A posteriori error estimator based on gradient recovery by averaging for convection-diffusion-reaction problems approximated by discontinuous Galerkin methods

2012 ◽  
Vol 33 (1) ◽  
pp. 212-241 ◽  
Author(s):  
E. Creuse ◽  
S. Nicaise
Keyword(s):  
Discontinuous Galerkin Methods ◽  
Posteriori Error ◽  
Diffusion Reaction ◽  
Error Estimator ◽  
Galerkin Methods ◽  
A Posteriori ◽  
Gradient Recovery ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Convection Diffusion

scholarly journals AN A POSTERIORI ERROR ESTIMATOR FOR hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC EIGENVALUE PROBLEMS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250030 ◽  
Author(s):  
STEFANO GIANI ◽  
EDWARD J. C. HALL
Keyword(s):  
Discontinuous Galerkin Methods ◽  
Eigenvalue Problems ◽  
Posteriori Error ◽  
Error Estimator ◽  
Galerkin Methods ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Elliptic Eigenvalue Problems

In this paper we present a residual-based a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. In particular, we use as a model problem the Laplace eigenvalue problem on bounded domains in ℝd, d = 2, 3, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual-based error estimator also for non-convex domains and use numerical experiments to show that, under an hp-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non-smooth eigenfunctions.

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