  We explore extended B-splines as a stable basis for isogeometric analysis
with trimmed parameter spaces. The stabilization is accomplished by an
appropriate substitution of B-splines that may lead to ill-conditioned system
matrices. The construction for non-uniform knot vectors is presented. The
properties of extended B-splines are examined in the context of interpolation,
potential, and linear elasticity problems and excellent results are attained.
The analysis is performed by an isogeometric boundary element formulation using
collocation. It is argued that extended B-splines provide a flexible and simple
stabilization scheme which ideally suits the isogeometric paradigm.
