Abstract
This chapter provides an overview of a posteriori error estimates. Most of the literature in numerical analysis is concerned with a priori error estimates, that is, a statement of form. For many problems, these a priori estimates are sufficient. There are a large number of problems where either they have not been established or they exist but are not adequate because ∥Y∥βis unknown. Nonlinear boundary value problems of the form arise in the study of chemically reacting systems with cylindrical symmetry; y is essentially the temperature and β is a dimensionless combination of other physical parameters. As problems of this type occur in a variety of applications, it is desirable to develop the theory of a posteriori error estimates.
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