Application of new error estimators based on gradient recovery and external domain approaches to 2D elastostatics problems

Abstract

Two new error estimators for the BEM in 2D potential problems were recently presented by the authors. This work extends these two error estimators for 2D elastostatics problems. The first approach involves a local error estimator based on a gradient recovery procedure in which the error function is based on differences between smoothed and non-smoothed rates of change of boundary variables in the local tangential direction. The second approach is associated with the external problem formulation and gives both local and global measures of the error, depending on a choice of the external evaluation point. These approaches are post-processing procedures. Both estimators show consistency with mesh refinement and give similar qualitative results. The error estimator using the gradient recovery approach presents a more general characteristic as its formulation does not rely on an ‘optimal’ choice of an external parameter, such as in the case of the external domain error estimator. Also, the external domain error estimator can be used only for domains in which an exterior region exists. For example, the external domain error estimator cannot be used for an infinite domain with a crack, because a point in the exterior region (inside the crack) will not be at a finite distance to the crack surface.