•  The goal of solution verification is to estimate and control, if possible, the error in each QOI for the simulation problem at hand.

•  The efficiency and effectiveness of code- and solution-verification processes can often be enhanced by exploiting the hierarchical composition of codes and solutions, verifying first the lowest-level building blocks and then moving successively to more complex levels.

•  Verification is most effective when performed on software developed under appropriate software quality practices. These include software-configuration management and regression testing.

3.5 REFERENCES

Ainsworth, M., and J.T. Oden. 2000. A Posteriori Error Estimation in Finite Element Analysis. New York: Wiley Interscience.

Almeida, J., and T. Oden. 2010. Solution Verification, Goal-Oriented Adaptive Methods for Stochastic Advection-Diffusion Problems. Computer Methods in Applied Mechanics and Engineering 199(37-40):2472-2486.

American National Standards Institute. 2005. American National Standards: Quality Management Systems—Fundamentals and Vocabulary ANSI/ISO/ASQ Q9001-2005. Milwaukee, Wisc.: American Society for Quality.

Ayewah, N., D. Hovemeyer, J.D. Morgenthaler, J. Penix, and W. Pugh. 2008. Using Static Analysis to Find Bugs. IEEE Software 25(5):22-29.

Babuska, I. 2004. Verification and Validation in Computational Engineering and Science: Basic Concepts. Computer Methods in Applied Mechanics and Engineering 193:4057-4066.

Babuska, I., and T. Strouboulis. 2001. The Finite Element Method and Its Reliability. Oxford, U.K.: Oxford University Press.

Bauman, P.T., J.T. Oden, and S. Prudhomme. 2009. Adaptive Multiscale Modeling of Polymeric Materials with Arlequin Coupling and Goals Algorithms. Computer Methods in Applied Mechanics and Engineering 198:799-818.

Becker, R., and R. Rannacher. 2001. An Optimal Control Approach to a Posteriori Error Estimation in Finite Element Methods. Acta Numerica 10:1-102.

Brezinski, C., and M. Redivo-Zaglia. 1991. Extrapolation Methods. Amsterdam, Netherlands: North-Holland.

Burstedde, C., O. Ghattas, T. Tu, G. Stadler, and L. Wilcox. 2009. Parallel Scalable Adjoint-Based Adaptive Solution of Variable-Viscosity Stokes Flow Problems. Computer Methods in Applied Mechanics and Engineering 198:1691-1700.

Burstedde, C., L.C. Wilcox, and O. Ghattas. 2011. Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees. SIAM Journal on Scientific Computing 33(3):1103-1133.

Cousot, P. 2007. The Role of Abstract Interpretation in Formal Methods. Pp. 135-137 in SEFM 2007, 5th IEEE International Conference on Software Engineering and Formal Methods, London, U.K., September 10-14. Mike Hinchey and Tiziana Margaria (Eds.). Piscataway, N.J.: IEEE Press.

DOE (Department of Energy). 2000. ASCI Software Quality Engineering: Goals, Principles, and Guidelines. DOE/DP/ASC-SQE-2000-FDRFT-VERS2. Washington, D.C.: Department of Energy.

DOE. 2005. Quality Assurance. DOE O414. Washington, D.C.: Department of Energy.

Estep, D., V. Carey, V. Ginting, S. Tavener, and T. Wildey. 2008. A Posteriori Error Analysis of Multiscale Operator Decomposition Methods for Multiphysics Models. Journal of Physics: Conference Series 125:1-16.

Jones, C. 2000. Software Assessments, Benchmarks, and Best Practices. Upper Saddle River, N.J.: Addison Wesley Longman.

Knupp, P., and K. Salari. 2003. Verification of Computer Codes in Computational Science and Engineering. Boca Raton, Fla.: Chapman and Hall/CRC.

McCormick, S. 1989. Multilevel Adaptive Methods for Partial Differential Equations. Philadelphia, Pa.: Society for Industrial and Applied Mathematics.

Oden, J.T. 2003. Error Estimation and Control in Computational Fluid Dynamics. Pp. 1-23 in The Mathematics of Finite Elements and Applications. J.R. Whiteman (Ed.). New York: Wiley.

Oden, J.T., and A. Prudhomme. 2001. Goal-Oriented Error Estimation and Adaptivity for the Finite Element Method. Computer Methods in Applied Mechanics and Engineering 41:735-756.

Oden, J.T., S. Prudhomme, A. Romkes, and P. Bauman. 2006. Multi-Scale Modeling of Physical Phenomena: Adaptive Control of Models. SIAM Journal on Scientific Computing 28(6):2359-2389.

Roache, P. 1998. Verification and Validation in Computational Science and Engineering. Albuquerque, N.Mex.: Hermosa Publishers.

Roache, P. 2002. Code Verification by the Method of Manufactured Solutions. Journal of Fluids Engineering 124(1):4-10.

Rüde, U. 1993. Mathematical and Computational Techniques for Multilevel Adaptive Methods. Philadelphia, Pa.: Society for Industrial and Applied Mathematics.

Westfall, L. 2010. Test Coverage: The Certified Software Quality Handbook. Milwaukee, Wisc.: ASQ Quality Press.



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