Applied Numerical Mathematics 52 (2005) 219–234 www.elsevier.com/locate/apnum On the importance and uses of feedback information in FEA Barna Szabó a,∗ , Ricardo Actis b a Center for Computational Mechanics, Washington University, Campus Box 1129, St. Louis, MO 63130, USA b Engineering Software Research and Development, Inc., 10845 Olive Boulevard, St. Louis, MO 63141, USA Available online 27 October 2004 Dedicated to Professor Joseph E. Flaherty on the occasion of his 60th birthday Abstract Procedures for verification and validation through adaptive control of the errors of discretization and idealization in finite element analysis (FEA), guided by feedback information, are discussed. A hierarchic framework for the construction of sequences of finite element spaces and working models is outlined and an example is presented.  2004 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: Finite elements; Mathematical models; Hierarchic models; Adaptivity; Feedback information; Verification; Validation 1. Introduction Adaptive methods continue to be a focus of interest in the field of finite element analysis. The term adaptivity has various meanings: in the broad (engineering) sense adaptivity is understood to be a process devised for efficient control of the errors of idealization and the errors of discretization to guarantee that the data of interest are computed to within a specific tolerance. Adaptivity in a restricted sense is understood to be a process for efficient control of the errors of discretization in terms of the data of interest for linear problems only. Adaptivity in the sense of the first research papers published on the subject was understood to mean a process by which the errors of discretization are controlled in linear elliptic problems in the energy norm only. See, for example, [5]. * Corresponding author. E-mail addresses: szabo@me.wustl.edu (B. Szabó), ricardo.actis@esrd.com (R. Actis). 0168-9274/$30.00  2004 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.apnum.2004.08.032