Quasi-Optimal Adaptive BEM
نویسندگان
چکیده
منابع مشابه
Convergence of Adaptive BEM and Adaptive FEM-BEM Coupling for Estimators Without h-Weighting Factor
We analyze adaptive mesh-refining algorithms in the frame of boundary element methods (BEM) and the coupling of finite elements and boundary elements (FEM-BEM). Adaptivity is driven by the two-level error estimator proposed by Ernst P. Stephan, Norbert Heuer, and coworkers in the frame of BEM and FEM-BEM or by the residual error estimator introduced by Birgit Faermann for BEM for weakly-singula...
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A conforming finite element method on polygonal meshes is introduced which handles hanging nodes naturally. Ansatz functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clément type a residual-based error estimate is obtained. This a posteriori estimator can be used to rate the accu...
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Galerkin methods for FEM and BEM based on uniform mesh refinement have a guaranteed rate of convergence. Unfortunately, this rate may be suboptimal due to singularities present in the exact solution. In numerical experiments, the optimal rate of convergence is regained when algorithms based on a-posteriori error estimation and adaptive mesh-refinement are used. This observation was proved mathe...
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We consider a (possibly) nonlinear interface problem in 2D and 3D, which is solved by use of various adaptive FEM-BEM coupling strategies, namely the Johnson-Nédélec coupling, the Bielak-MacCamy coupling, and Costabel’s symmetric coupling. We provide a framework to prove that the continuous as well as the discrete Galerkin solutions of these coupling methods additionally solve an appropriate op...
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In the numerical treatment of integral equations of the first kind using boundary element methods (BEM), the author and E. P. Stephan have derived a posteriori error estimates as tools for both reliable computation and self-adaptive mesh refinement. So far, efficiency of those a posteriori error estimates has been indicated by numerical examples in model situations only. This work affirms effic...
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