Local error estimates for adaptive mesh refinement

Five methods for local error estimation in a finite-element solution for adaptive meshing are analyzed. All these methods are a-posteriori, single-solution, element-by-element error estimators. Two are based on the estimation of the first neglected term in the series expansion of the solution, a third is based on the approximate solution of a local boundary-value problem with hierarchical shape functions, and the other two utilize a residual evaluation. All the methods are described and implemented in a common environment, and the results obtained in a simple test case are presented and discussed