AN ASYMPTOTICALLY EXACT, POINTWISE, A-POSTERIORI ERROR ESTIMATOR FOR LINEAR, ELLIPTIC, ONE-DIMENSIONAL PROBLEMS WITH POSSIBLE SINGULARITIES IN THE SOLUTION

[摘要] When the finite-element solution of a variational problem possesses certain superconvergence 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 found, and its convergence properties proved in the special case of one-dimensional, linear, elliptic problems. Special attention is given to the effects of the appearance of singularities and zeros of derivatives in the exact solution.

[发布日期] 1994-09-30

[关键词] POINTWISE;A POSTERIORI;ERROR ESTIMATOR;SINGULAR SOLUTION;FINITE-ELEMENT METHOD