On Locking and Robustness in the Finite Element Method
MARYLAND UNIV COLLEGE PARK INST FOR PHYSICAL SCIENCE AND TECHNOLOGY
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A numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value. A robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter. We develop precise mathematical definitions for these terms, give their quantitative characterization and prove some general theorems involving locking and robustness. A model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described. Applications of our theory to some different problems involving locking are presented.
- Numerical Mathematics