(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Bartels, Sören; Müller, Rüdiger
A fully computable upper bound for the finite element approximation
error of Allen-Cahn and Cahn-Hilliard equations with logarithmic potentials
is derived. Numerical experiments show that for the sharp interface limit
this bound is robust past topological changes. Modifications of the abstract
results to derive quasi-optimal error estimates in different norms for lowest
order finite element methods are discussed and lead to weaker conditions on
the residuals under which the conditional error estimates hold.
