A combined rh-adaptive scheme based on domain subdivision. Formulation andlinear examples

An adaptive scheme is proposed in which the domain is split into two subdom ains. One subdomain consists of regions where the discretization is refined with an h-adaptive approach, whereas in the other subdomain node relocatio n or r-adaptivity is used. Through this subdivision the advantageous proper ties of both remeshing strategies (accuracy and low computer costs, respect ively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the appro ach suitable for coupling with various error assessment tools. Two-dimensio nal linear examples where the analytical solution is known illustrate the a pproach. It is shown that the combined rh-adaptive approach is superior to its components r- and h-adaptivity, in that higher accuracies can be obtain ed compared to a purely r-adaptive approach, while the computational costs are lower than that of a purely h-adaptive approach. As such, a more flexib le formulation of adaptive strategies is given, in which the relative impor tance of attaining a pre-set accuracy and speeding-up the computational pro cess can be set by the user. Copyright (C) 2001 John Wiley & Sons, Ltd.