When the finite element solution of a variational problem possesses certain super convergence properties, it is possible very inexpensively 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 in whatever norm is preferred, or if no error estimation is wanted it can be used for postprocessing of the solution to improve the quality. In this paper such a correction term is described for the general case of n dimensional, linear or nonlinear problems. Computational evidence of the performance in one space dimension is given with special attention to the effects of the appearance of singularities and zeros of derivatives in the exact solution.

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