Robust residual-based a posteriori error estimators for mixed finite   element methods for fourth order elliptic singularly perturbed problems
  We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the perturbation parameter. Robust residual-based a posteriori estimators for the new measure are obtained, which are achieved via a novel analytical technique based on an approximation result. Numerical examples are presented to validate our theory. 
Shaohong Du, Runchang Lin, Zhimin Zhang
math.NA