Summary: A posteriori error estimates for parabolic variational inequalities
, FrŽedŽeric Hecht
, David Pommier
July 12, 2008
We study a posteriori error estimates in the energy norm for some parabolic obstacle
problems discretized with a Euler implicit time scheme combined with a finite element spatial
approximation. We discuss the reliability and efficiency of the error indicators, as well as
their localization properties. Apart from the obstacle resolution, the error indicators vanish
in the so-called full contact set. The case when the obstacle is piecewise affine is studied
before the general case. Numerical examples are given.
Keywords: parabolic obstacle problems, finite element methods, a posteriori error estimates,
adaptive mesh refinement
This work is concerned with a posteriori error estimates in the energy norm for the numeri-
cal solutions of parabolic obstacle problems allowing for space/time mesh adaptive refinement.
These estimates are based on a posteriori error indicators which can be computed from the
solution of the discrete problem. Good error indicators should have two properties: reliability