Finite element formulation with high-order absorbing boundary conditions for time-dependent waves

The Hagstrom–Warburton high-order absorbing boundary conditions (ABCs) are considered. They are based on a high-order form of the Higdon ABCs using auxiliary variables and constitute a modification of the previously proposed Givoli–Neta ABCs. Here the Hagstrom–Warburton ABCs, which were originally used in a finite difference scheme, are incorporated into a finite element formulation. Exterior time-dependent problems are considered with rectangular computational domains. Special corner conditions are used in conjunction with the ABCs to make the truncated problem well-posed. The properties of the Hagstrom–Warburton and Givoli–Neta formulations are compared, and the relations between the two formulations are established. Numerical examples demonstrate the performance of the Hagstrom–Warburton finite element scheme.