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

Abstract

An adaptive scheme is proposed in which the domain is split into two subdomains. One subdomain consists of regions where the discretization is refined with an h-adaptive approach, whereas in the other subdomain node relocation or r-adaptivity is used. Through this subdivision the advantageous properties of both remeshing strategies (accuracy and low computer costs, respectively) can be exploited in greater depth. The subdivision of the domain is based on the formulation of a desired element size, which renders the approach suitable for coupling with various error assessment tools. Two-dimensional linear examples where the analytical solution is known illustrate the approach. It is shown that the combined rh-adaptive approach is superior to its components r- and h-adaptivity, in that higher accuracies can be obtained 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 flexible formulation of adaptive strategies is given, in which the relative importance of attaining a pre-set accuracy and speeding-up the computational process can be set by the user.