An Error Indicator Monitor Function for an r-Adaptive Finite-Element Method

An r-adaptive finite-element method based on moving-mesh partial differential equations (PDEs) and an error indicator is presented. The error indicator is obtained by applying a technique developed by Bank and Weiser to elliptic 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 obtained with the current method and the commonly used method based on solution gradients are presented and analyzed for several examples.