scholarly journals An Equilibrated A Posteriori Error Estimator for the Interior Penalty Discontinuous Galerkin Method

2014 ◽  
Vol 52 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
D. Braess ◽  
T. Fraunholz ◽  
R. H. W. Hoppe
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Interior Penalty ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem

2021 ◽  
Vol 36 (6) ◽  
pp. 313-336
Author(s):  
Ronald H. W. Hoppe ◽  
Youri Iliash
Keyword(s):  
Discontinuous Galerkin ◽  
Galerkin Approximation ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Interior Penalty ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Flux Function

Abstract We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the p-Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W 1,p norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.

scholarly journals Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems

2019 ◽  
Vol 144 (3) ◽  
pp. 585-614
Author(s):  
Joscha Gedicke ◽  
Arbaz Khan
Keyword(s):  
Discontinuous Galerkin ◽  
Eigenvalue Problems ◽  
Convergence Rates ◽  
A Priori ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

AbstractIn this paper, we present a divergence-conforming discontinuous Galerkin finite element method for Stokes eigenvalue problems. We prove a priori error estimates for the eigenvalue and eigenfunction errors and present a residual based a posteriori error estimator. The a posteriori error estimator is proven to be reliable and (locally) efficient. We finally present some numerical examples that verify the a priori convergence rates and the reliability and efficiency of the residual based a posteriori error estimator.

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