Error Estimates for Non-Linear Finite Element Computations.
PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS
Pagination or Media Count:
In recent years, increasing interest has centered on the development of reliable and computationally inexpensive a posteriori error estimates for finite element computations. Such estimates can provide some, often critically important, information about the accuracy and reliability of the computed solution as a model of the behavior of the physical phenomena under study. At the same time it has become widely accepted that these estimates also constitute a basic tool in the construction of efficient adaptive finite element processes which are designed to achieve a desired error tolerance at minimal cost or a best possible solution within an allowable cost range, Up to now most of this work concerned linear problems. Not unexpectedly, for non-linear problems the situation is much more difficult and the theory is by far not as well developed. In part this is due to the many special features of non-linear problems not present in the linear case. In particular, such problems usually involve a number of intrinsic parameters and --because of the non-linear nature -- interest centers rarely on the determination of a few specific solutions for fixed parameter values but instead on a more general study of these solutions under various changes of the parameters. This paper presents a new approach to the construction of a posteriori error estimates for non-linear problems which is highly effective and at the same time computationally rather inexpensive.
- Numerical Mathematics