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M. Aurada, M. Ebner, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:
"HILBERT - a MATLAB implementation of adaptive BEM";
in: "ASC Report 44/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

The Matlab BEM library HILBERT allows the numerical solution of the 2D Laplace
equation on some bounded Lipschitz domain with mixed boundary conditions by use of an
adaptive Galerkin boundary element method (BEM). This paper provides a documentation of
HILBERT. The reader will be introduced to the data structures of HILBERT and mesh-refinement
strategies. We discuss our approach of solving the Dirichlet problem (Section 5), the Neumann
problem (Section 6), and the mixed boundary value problem with Dirichlet and Neumann
boundary conditions (Section 7). Besides a brief introduction to these problems, their equivalent
integral formulations, and the corresponding BEM discretizations, we put an emphasis on
possible strategies to steer an adaptive mesh-refining algorithm. In particular, various error
estimators are discussed. Another notable feature is a complete and detailed description of our
Matlab implementation which enhances the reader´s understanding of how to use the HILBERT
program package.

http://www.asc.tuwien.ac.at/preprint/2009/asc44x2009.pdf