Finite element formulation with high-order absorbing boundary conditions for time-dependent waves. (English) Zbl 1125.76040

Summary: 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.


76M10 Finite element methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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