Abstract
The reliability of computer predictions of physical events depends on several factors: the mathematical model of the event, the numerical approximation of the model, and the random nature of data characterizing the model. This paper addresses the mathematical theories, algorithms, and results aimed at estimating and controlling modeling error, numerical approximation error, and error due to randomness in material coefficients and loads. A posteriori error estimates are derived and applications to problems in solid mechanics are presented.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 195-204 |
| Number of pages | 10 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 194 |
| Issue number | 2-5 SPEC. ISS. |
| DOIs | |
| State | Published - Feb 4 2005 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work has been supported by an ITR grant 0205181 from National Science Foundation and by grant N00014-95-0401 from the Office of Naval Research. The calculation presented were done by Drs. Fabio Nobile and Yusheng Feng who implemented algorithm to estimate error due to uncertainty based on software developed by Dr. Leszek Demkowicz. Drs. Nobile’s and Tempone’s work was supported by an ICES Post Doctoral Fellowship Program. The adaptive quadrature algorithm used to compute bound in (5.3c) on uncertainty error was developed and implemented by Drs. Nobile and Tempone. The bounds used on the variances in the coefficients were the result of experimental tests performed by Dr. Kenneth Liechti and P. Hosatte. Drs. Leszek Demkowicz, and James C. Browne provided valuable advice during the course of this work.
Keywords
- Adaptive modeling
- Modeling error estimation
- Stochastic partial differential equations
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications