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M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:
"Hilbert (Release 2): A MATLAB implementation of adaptive BEM";
in: "ASC Report 14/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

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, the Neumann
problem, the mixed boundary value problem with Dirichlet and
Neumann boundary conditions, and the extension to problems with
non-homogeneous volume forces. 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/2010/asc14x2010.pdf