A p-adaptive algorithm for the BEM with the hypersingular operator
on the plane screen
Norbert Heuer, Mario E. Mellado, Ernst P. Stephan
Internat. J. Numer. Methods Engrg. 53 (1), 85-104, 2002.
We propose a p-adaptive algorithm for the Galerkin method
solving hypersingular integral operators on surfaces.
The error indicators/estimators are based on projections
of the actual error onto local subspaces. These subspaces
are defined by decompositions of specially designed enriched
ansatz spaces.
Our algorithm uses different strategies for the refinement
and the stopping criterion. The error estimator that stops
the algorithm is based on an overlapping decomposition of
an ansatz space that is defined by mesh refinement.
The error indicators that steer the p-refinement are computed
via an almost direct decomposition of an enriched ansatz space that
uses the same mesh but higher polynomial degrees.
Numerical results support the efficiency of our algorithm.