ROBUST AND EXPLICIT A POSTERIORI ERROR ESTIMATION TECHNIQUES IN ADAPTIVE FINITE ELEMENT METHOD
thesisposted on 13.08.2019 by Difeng Cai
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
The thesis presents a comprehensive study of a posteriori error estimation in the adaptive solution to some classical elliptic partial differential equations. Several new error estimators are proposed for diffusion problems with discontinuous coefficients and for convection-reaction-diffusion problems with dominated convection/reaction. The robustness of the new estimators is justified theoretically. Extensive numerical results demonstrate the robustness of the new estimators for challenging problems and indicate that, compared to the well-known residual-type estimators, the new estimators are much more accurate.