On goal-oriented error estimation for elliptic problems: application to the control of pointwise errors Original Research Article

A method to estimate and control pointwise errors in finite element approximations of elliptic problems is presented as an application of the more general theory of goal-oriented error estimation. In the latter, the accuracy of numerical approximations is assessed in terms of measures that are of practical interest to engineers rather than the classical global energy norm. Goal-oriented error estimation requires the solution of a problem dual to the original problem and the computation of several global error estimates. The performance of the method is carefully tested in the particular case of estimation and control of pointwise errors on a one-dimensional problem.