An Adaptive Finite Element Method for the Wave Scattering with Transparent Boundary Condition

An Adaptive Finite Element Method for the Wave Scattering with Transparent Boundary Condition Consider the acoustic wave scattering by an impenetrable obstacle in two dimensions. The model is formulated as a boundary value problem for the Helmholtz equation with a transparent boundary condition. Based on a duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated Dirichlet-to-Neumann boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of boundary operator which decays exponentially with respect to the truncation parameter. A new adaptive finite element algorithm is proposed for solving the acoustic obstacle scattering problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are marked through the finite element discretization error. Numerical experiments are presented to illustrate the competitive behavior of the proposed adaptive method. Journal of Scientific Computing Springer Journals

An Adaptive Finite Element Method for the Wave Scattering with Transparent Boundary Condition

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Springer US
Copyright © 2017 by Springer Science+Business Media New York
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
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