Abstract
In this article, we describe our general concept of residual-based error estimation and adaptive mesh generation for finite element Galerkin methods. Motivated by applications in fluid and structural mechanics, our objective is to derive error bounds with respect to general functionals of the solution which represent the physical quantities to be computed. Using duality arguments as known from the a priori error analysis of finite element methods, we obtain a posteriori error estimates in which local residuals of the computed solution are multiplied by weights obtained from the corresponding dual solution. These weighted error estimators explicitly contain local information about the mechanism of error propagation while in the conventional energy-type estimators this information is condensed into a global stability constant. In this way, we achieve strategies for constructing most economical meshes together with useful error bounds for the quantities of interest. This method is introduced here first for a simple model case and is then further illustrated by two examples from fluid and structural mechanics.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call