A residual based error estimator using radial basis functions

In this paper, a novel residual based error estimator using radial basis functions (RBFs) is proposed. The error estimator evaluates the residual in the strong-form governing equation in the local domain through direct integration. Due to the higher order continuous feature of the RBFs, the higher derivatives of the field function in the strong-form governing equation can be obtained using RBFs. The numerical examples show that the new residual based error estimator is simple, versatile robust and yet effective in the adaptive analyses. It is not only suitable for adaptive analysis that uses numerical method formulated based on mesh, e.g. finite element method, but also meshfree methods where the conventional residual based and recovery based error estimator cannot be used. Furthermore the present error estimator is also feasible for numerical method that is formulated based on both strong and weak formulation in the adaptive analyses.