{'fraction_non_alphanumeric': 0.017351598173515982, 'fraction_numerical': 0.0, 'mean_word_length': 5.372093023255814, '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}}
An A Posteriori Error Estimator for the FEM in Nonlinear Elastostatics

In this paper we deal with static problems of geometrically nonlinear elasticity. For the more challenging problems of this type, adaptive finite element methods are needed. A crucial ingredient for these methods is a robust and efficient a posteriori error estimator. In most implementations the well-known error estimators for linear elasticity are applied to a linearization of the nonlinear problems under consideration. But these linearized estimators work only for mildly nonlinear problems.In geometrically nonlinear elastostatics a coarse grid approximation can be used to resolve the main features of the solution.Using that fact and Verfurth's error estimator analysis we develop a new estimator, which uses coarse-grid projections of the operators. Our estimator is shown to be efficient, even in the presence of strong nonlinearities, especially around simple limit points, where the linearized estimators break down. To illustrate its performance we present numerical results derived from a planar elasticit...