A posteriori h-hierarchical adaptive scaled boundary finite element method (ASBFEM) for transient elastodynamic problems is developed. In a time step, the fields of displacement, stress, velocity and acceleration are all semi-analytical and the kinetic energy, strain energy and energy error are all semi-analytically integrated in subdomains. This makes mesh mapping very simple but accurate. Adaptive mesh refinement is also very simple because only subdomain boundaries are discretised. Two 2D examples with stress wave propagation were modelled. It is found that the degrees of freedom needed by the ASBFEM are only 5%–15% as needed by adaptive FEM for the examples.
Yang, J., Zhang, ZH., Liu, GH., & Ooi, ET. (2011). An h-hierarchical adaptive scaled boundary finite element method for elastodynamic problems. Computers & Structures, 89(13-14), 1417-1429. https://doi.org/10.1016/j.compstruc.2011.03.006