  We analyze the error of the WEB-S finite element method applied to elliptic
systems with non-cooperative dominant coupling,with a mixed
Dirichlet/Neumann/Robin boundary condition. This problem is strongly related to
a posteriori error estimates, giving computable bounds for computational errors
and detecting zones in the solution domain where such errors are too large and
certain mesh refinements should be performed. These results are based on an
extensive regularity analysis of the interface problems of concern.Finally, the
error analysis is illustrated by numerical experiments.
