An error indicator monitor function for an r-adaptive finite-element method

An r-adaptive finite-element method based on moving-mesh partial differenti al equations (PDEs) and an error indicator is presented. The error indicato r is obtained by applying a technique developed by Bank and Weiser to ellip tic equations which result in this case from temporal discretization of the underlying physical PDEs on moving meshes. The construction of the monitor function based on the error indicator is discussed. Numerical results obta ined with the current method and the commonly used method based on solution gradients are presented and analyzed for several examples. (C) 2001 Academ ic Press.