Energy norm based a posteriori error estimation for boundary element methods in two dimensions
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Cited by (30)
The saturation assumption yields optimal convergence of two-level adaptive BEM
2020, Applied Numerical MathematicsCitation Excerpt :A well-known disadvantage of this class of estimators is that the crucial upper error bound (usually referred to as reliability of the estimator) relies on a so-called saturation assumption (see, e.g., (6) below) and, in many situations, is even equivalent to that. However, two-level error estimators and related adaptive strategies perform strikingly well in practice; see, e.g., [13,28–30,45,52]. The purpose of the present work is to shed some light on this empirical observation.
Hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems
2014, Computers and Mathematics with ApplicationsA posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems
2014, Applied Numerical MathematicsZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve
2014, Engineering Analysis with Boundary ElementsCitation Excerpt :Numerical analysis of adaptive BEM was initiated by the pioneering works [48–51]. By now, available error estimators from the literature include residual-based error estimators for weakly singular [19,20,10,12,15,26,27] and hyper-singular integral equations [20,10,14], hierarchical error estimators for weakly singular [25,32,39] and hyper-singular integral equations [31,32], (h−h/2)-based error estimators [24,23,29], averaging on large patches [16–18], and estimators based on the use of the full Calderón system [21,22,34,37,41,43]. The reader is also referred to the overviews given in [12,23,35] and the references therein.
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
2014, Journal of Computational and Applied MathematicsA new conservative numerical scheme for flow problems on unstructured grids and unbounded domains
2013, Journal of Computational Physics