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

Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in defining monitor functions for the r-adaptive finite element methods based on moving mesh partial differential equations. The methods are compared with a careful selection of examples. The numerical results show that the methods based on both interpolation errors and a posteriori error estimates work well and have better performance than that based on the solution gradient. Since, the interpolation error is in general easier and more economic to compute than a posteriori error estimates, this study suggests that the error indicator based on interpolation errors be used for the r-adaptive method.