Accounting for stability: a posteriori error estimates based on residuals and variational analysis

Donald Estep, Colorado State University

Over the last two decades, there has been a revolution in computational error estimation and adaptive error control in engineering by means of residual-dual based a posteriori error estimates. In particular, this new approach yields a direct account of the effects of stability on the accumulation and propagation of error through space and time and so yields an estimate of the true global error. I will describe this new approach in friendly terms and then discuss a couple of particular applications that are fun and illuminating.