Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 346, Issue -, Pages 260-287Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2018.12.006
Keywords
Boundary element method; Helmholtz equation; A posteriori error estimate; Adaptive algorithm; Convergence; Optimality
Funding
- EPSRC [EP/P013791/1]
- Austria Science Fund (FWF) through the research project Optimal adaptivity for BEM and FEM-BEM coupling [P27005]
- Austria Science Fund (FWF) through the research program Taming complexity in partial differential systems [SFB F65]
- EPSRC [EP/P013791/1, EP/K03829X/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K03829X/1] Funding Source: researchfish
- Austrian Science Fund (FWF) [P27005] Funding Source: Austrian Science Fund (FWF)
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We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is steered by a residual error estimator and does not rely on any a priori information that the underlying meshes are sufficiently fine. We prove convergence of the error estimator with optimal algebraic rates, independently of the (coarse) initial mesh. As a technical contribution, we prove certain local inverse-type estimates for the boundary integral operators associated with the Helmholtz equation. (C) 2018 Elsevier B.V. All rights reserved.
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