A POSTERIORI ERROR ESTIMATES FOR ELLIPTIC OBSTACLE PROBLEM: A SUBJECT FIELD REVIEW

The problem of obtaining a posteriori estimates for various types of tasks was posed quite a long time ago, when a huge number of tasks began to appear, the exact solution of which is very often impossible to find. That is why the development of methods for obtaining a posteriori estimates has begun, which are based exclusively on the data that were obtained in the process of constructing an approximate solution. In this subject field review, error estimates for an elliptic problem with an obstacle are considered. The purpose of this work is to generalize the results obtained earlier, based on three existing methods for obtaining a posteriori estimation: the method of residuals, the gradient averaging method and the method of dual majorants. The objective of this work is to identify the strengths and weaknesses of each method separately. To extract documents, the Scopus platform was used, on which articles were selected in accordance with the developed search criteria. 30 papers were extracted to write a systematic review. 16 of them are devoted to the method of residuals, 11 to the method of gradient averaging and 3 to the method of dual majorants. In addition, only 4 papers present pure theory without numerical experiments, all the others (N=26) have numerical results. Positive and negative sides were identified for all these methods. Each of them has its own characteristics and disadvantages. The limits of applicability of these methods were also revealed, and guaranteed estimates of the deviation rate of approximate solutions that are effective were obtained. The results of this review can be used by a wide range of specialists dealing with this problem.