Comparison of two-dimensional r-adaptive finite element methods using various error indicators

Error indicators based on solution gradients, interpolation errors, and a p osteriori error estimates are presented for use in defining monitor functio ns for the r-adaptive finite element methods based on moving mesh partial d ifferential equations. The methods are compared with a careful selection of examples. The numerical results show that the methods based on both interp olation errors and a posteriori terror estimates work well and have better performance than that based on the solution gradient. Since, the interpolat ion error is in general easier and more economic to compute than a posterio ri error estimates, this study suggests that the error indicator based on i nterpolation errors be used for the r-adaptive method. (C) 2001 Published b y Elsevier Science B.V. on behalf of IMACS.