A p-adaptive multi-node extended multiscale finite element method for 2D elastostatic analysis of heterogeneous materials

► A multi-node extended multiscale finite element method is developed for 2D elastostatic analysis of heterogeneous materials. ► A kind of coarse element with more than four macroscopic nodes is proposed in the developed multiscale method. ► An adaptive algorithm is presented for the coarse-scale mesh. ► Some numerical experiments are carried out to illustrate the effectiveness of the developed multiscale method and the presented adaptive algorithm.