Coupling of finite and boundary element methods for an elastoplastic interface problem
SIAM Journal on Numerical Analysis
On the Dirichlet problem in elasticity for a domain exterior to an arc
Journal of Computational and Applied Mathematics
A posteriori error estimates for boundary element methods
Mathematics of Computation
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
An a posteriori error estimate for a first-kind integral equation
Mathematics of Computation
SIAM Journal on Scientific Computing
Convergence of adaptive BEM for some mixed boundary value problem
Applied Numerical Mathematics
Estimator reduction and convergence of adaptive BEM
Applied Numerical Mathematics
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
Journal of Computational and Applied Mathematics
A posteriori error estimates of hp-adaptive IPDG-FEM for elliptic obstacle problems
Applied Numerical Mathematics
hp-adaptive IPDG/TDG-FEM for parabolic obstacle problems
Computers & Mathematics with Applications
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A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. We analyze the mathematical relation between the h-h/2-error estimator from [S. Ferraz-Leite, D. Praetorius, Simple a posteriori error estimators for the h-version of the boundary element method, Computing 83 (2008) 135-162], the two-level error estimator from [S. Funken, Schnelle Losungsverfahren fur FEM-BEM Kopplungsgleichungen, Ph.D. thesis, University of Hannover, 1996 (in German); P. Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R^3, Computing 60 (1998) 243-266], and the averaging error estimator from [C. Carstensen, D. Praetorius, Averaging techniques for the effective numerical solution of Symm's integral equation of the first kind, SIAM J. Sci. Comput. 27 (2006) 1226-1260]. We essentially show that all of these are equivalent, and we extend the analysis of [S. Funken, Schnelle Losungsverfahren fur FEM-BEM Kopplungsgleichungen, Ph.D. thesis, University of Hannover, 1996 (in German); P. Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R^3, Computing 60 (1998) 243-266] to cover adaptive mesh-refinement. Therefore, all error estimators give lower bounds for the Galerkin error, whereas upper bounds depend crucially on the saturation assumption. As model examples, we consider first-kind integral equations in 2D with weakly singular integral kernel.