An asymptotically exact, pointwise, a posteriori error estimator for linear, elliptic, one-dimensional problems with possible singularities in the solution (Q1347149)

This paper deals with the finite element solution of a variational problem which possesses certain superconvergence properties. It is possible to obtain a correction term providing an additional order of approximation of the solution. The correction can be used for error estimation locally or globally. Here a correction term is found with the convergence properties in the special case of one-dimensional linear elliptic problems. The author gives special attention to the effects of the appearance of singularities and zeros of derivatives in the exact solution. Some computational results are included.