A residual-based a posteriori error estimator for Ciarlet-Raviart formulation of the first biharmonic problem (Q2785817)

This paper deals with the application of Verfürth methodology to the so-called ``psi-omega'' (Ciarlet-Raviart) mixed finite element approximation of the first biharmonic equation NEWLINE\[NEWLINE\Delta^2u= f\text{ in } \Omega, \quad u= {\partial u\over\partial n} =0 \quad \text{ on } \Gamma=\partial\Omega.NEWLINE\]NEWLINE The use of automatic, self-adaptive mesh refinement techniques based on a posteriori error estimators is now a common feature of many of the high-level finite element codes used for numerical simulation in fluid and solid mechanics. The authors show how an appropriate modification of the mentioned methodology gives the proper scaling of the residuals leading to both lower and upper estimation. The presentation of five numerical examples that illustrate the efficiency of the residual estimator is concluded.