Accounting for stability: accurately estimating the error of
numerical solutions of differential equations
Abstract
Accurately estimating the error of numerical solutions of
differential equations remains an important scientific
problem. Recently, we have made significant progress using
a new approach which at the heart is computational rather
than analytical. This approach is based on a variational a
posteriori error analysis that takes into account both the
local introduction of discretization error and the
accumulation of errors. I will explain the ingredients of
this theory and illustrate its application using a variety
of examples.
