{'fraction_non_alphanumeric': 0.04648074369189907, 'fraction_numerical': 0.025896414342629483, 'mean_word_length': 4.751908396946565, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A posteriori error estimates taking into account indeterminacy of the problem data

In many cases, values of the problem data (coefficients of a differential equation, boundary conditions, and right–hand sides) are not given exactly. In practical problems, we only know that they belong to certain sets of possible data values. Therefore estimation of errors of the approximate solution must take into account not only the approximation error, but also those arising due to indeterminacy of the data. The objective of this paper is to introduce a general scheme for deriving a posteriori estimates of this type. The method is based upon using functional-type a posteriori estimates that have been earlier derived in [(S. Repin, A posteriori error estimation for nonlinear variational problems by duality theory. Zap. Nauch. Semin., St. Petersburg Branch of V. A. Steklov Institute of Mathematics (1997) 243, 201–214.), (S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp. (2000) 69, No. 230, 481–500.), (S. Repin, Two-sided estimatesof deviations from exact solutions for uniformly elliptic equations. Transactions of St. Petersburg Math. Soc. (2001) 9, 148–179 (in Russian).)] and some other papers for boundary-value problems with operators of elliptic type. Estimates obtained in the paper are of two types. They show the errors in the worst- and best-case situations depending on the way the data error is combined with the approximation one.