The New Gradient Recovery And External Domain Error Estimators: Extension To 2-D Elastostatics Bem

Abstract

Two new error estimators for the BEM in 2-D potential problems were recently
presented by the authors. This work extends these two error estimators for 2-D 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-processingpr ocedures. 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.