scholarly journals Mesh adaptivity for quasi‐static phase‐field fractures based on a residual‐type a posteriori error estimator

2019 ◽  
Vol 43 (1) ◽  
Author(s):  
K. Mang ◽  
M. Walloth ◽  
T. Wick ◽  
W. Wollner
Keyword(s):  
Phase Field ◽  
Type A ◽  
Posteriori Error ◽  
Error Estimator ◽  
Mesh Adaptivity ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Static Phase

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.

Sign in / Sign up

Export Citation Format

Share Document