  We study the optimal approximation of the solution of an operator equation by
certain n-term approximations with respect to specific classes of frames. We
study worst case errors and the optimal order of convergence and define
suitable nonlinear frame widths.
  The main advantage of frames compared to Riesz basis, which were studied in
our earlier papers, is the fact that we can now handle arbitrary bounded
Lipschitz domains--also for the upper bounds.
  Key words: elliptic operator equation, worst case error, frames, nonlinear
approximation, best n-term approximation, manifold width, Besov spaces on
Lipschitz domains
