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Comput. Methods Appl. Mech. Engrg. 193 (2004) 4057–4066

Verification and validation in computational engineering and science: basic concepts
Ivo Babuska, J. Tinsley Oden
Institute for Computational Engineering and Sciences, The University of Texas at Austin, 1 University Station, Campus Code 0200, Austin, TX 78712, USA

1. Introduction Computationalengineering and science, the discipline concerned with the use of computational methods and devices to simulate physical events and engineering systems, is being heralded by many as one of the most important developments in recorded history [11]. Computer predictions of physical events, it is argued, can be of enormous importance in making critical decisions that affect every facet of human existence. As thespeed and capacity of computer systems continue to grow, the expectations of users of computer models in decision making continues to grow in kind. Today, some look toward computer-based predictions as a means to obtain vital quantitative information on events that influence the security, health, and well being of much of mankind and many nations and that influence the success of major businessesand other enterprises worldwide. It is understandable that the reliability of computer predictions has been an issue of growing concern for several decades. Major questions that arise with increasing frequency are ‘‘can computer predictions be used as a reliable bases for crucial decisions? How can one assess the accuracy or validity of a computer prediction? What confidence can be assigned to acomputer prediction of a complex event?’’ The collection of processes, philosophical issues, and procedures connected with answering these questions has become known as the subject of verification and validation (V&V), the verification process addressing the quality of the numerical treatment of the model used in the prediction and the validation process addressing the quality of the model. V&V hasbeen the focus of much study and debate for many years, and a relatively large literature exists on the subject. Among noteworthy works on the subject in the engineering literature are the book of Roache [14], the survey articles of Oberkampf and collaborators, e.g. [9,10], the AIAA standards on the subject as it applies to computational and fluid dynamics [3]. Many other relevant references are citedin these works. Closely akin to works on V&V are those on risk analysis prelevant in applications in, for example, civil engineering [6,7], nuclear engineering [4,13], and in environmental engineering and sciences [2]. The broad interest in V&V in many different scientific and technological areas has led to a diverse and often incompatible list of definitions and concepts as it pertains to differentdisciplines. Moreover, despite the fact that modern views of the subject have been under development for nearly a decade, much remains to be done toward developing concrete approaches for implementing V&V procedures for particular applications.

Corresponding author. Tel.: +1-512-471-3312; fax: +1-512-471-8694. E-mail address: (J.T. Oden).

0045-7825/$ - see frontmatter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cma.2004.03.002


I. Babuska, J.T. Oden / Comput. Methods Appl. Mech. Engrg. 193 (2004) 4057–4066

In the present paper, we attempt to present a foundation for V&V as it applies to simulations in mechanics and physics. Our goal is to provide definitions, concepts, and principles that will facilitate communication of ideas andprecision of thought regarding the reliability of computer simulations of physical events of interest in computational mechanics and physics. We will then propose specific procedures for implementing V&V processes. We are not concerned with V&V in its broadest (and vaguest) context (modeling manufacturing systems, stock market trends, economics, battle-field models, etc.): Our interest lies totally...