Concepts of an adaptive hierarchical finite element code
IMPACT of Computing in Science and Engineering
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
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
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Energy norm based a posteriori error estimation for boundary element methods in two dimensions
Applied Numerical Mathematics
Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators
Numerische Mathematik
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
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For a boundary integral formulation of the 2D Laplace equation with mixed boundary conditions, we consider an adaptive Galerkin BEM based on an (h-h/2)-type error estimator. We include the resolution of the Dirichlet, Neumann, and volume data into the adaptive algorithm. In particular, an implementation of the developed algorithm has only to deal with discrete integral operators. We prove that the proposed adaptive scheme leads to a sequence of discrete solutions, for which the corresponding error estimators tend to zero. Under a saturation assumption for the non-perturbed problem which is observed empirically, the sequence of discrete solutions thus converges to the exact solution in the energy norm.