| Popis: |
This paper presents application of the equilibrated residual method (ERM) of a posteriori error estimation to the elliptic problems of elasticity (elastostatics) and dielectricity (electrostatics), and to the coupled problem of (stationary) piezoelectricity as well. It has been shown in numerous works that the direct application of the method based on the linear equilibration may lead to unacceptable overestimation of the errors. In this preliminary work, we show how to tune the estimators in order to obtain reasonable results of the estimation. We address the approximation and total error estimation within the mentioned two uncoupled and one coupled problem. The modeling error is defined as a difference between the previous two errors for each of three problems. We focus on three issues in the paper. The first one is comparison of the existing methods of liner equilibration. The second one is the assessment of the application of the higher order equilibration. Finally, the third one is the effectivity assessment of the estimation for some chosen promising variants of the equilibration, which leads to the equilibrated residual methods tuned for particular applications. |
