  There are many application papers that solve elliptic boundary value problems
by meshless methods, and they use various forms of generalized stiffness
matrices that approximate derivatives of functions from values at scattered
nodes $x_1,\ldots,x_M\in \Omega\subset\R^d$. If $u^*$ is the true solution in
some Sobolev space $S$ allowing enough smoothness for the problem in question,
and if the calculated approximate values at the nodes are denoted by $\tilde
u_1,\ldots,\tilde u_M$, the canonical form of error bounds is $$ \max_{1\leq
j\leq M}|u^*(x_j)-\tilde u_j|\leq \epsilon \|u^*\|_S $$ where $\epsilon$
depends crucially on the problem and the discretization, but not on the
solution. This contribution shows how to calculate such $\epsilon$ {\em
numerically and explicitly}, for any sort of discretization of strong problems
via nodal values, may the discretization use Moving Least Squares, unsymmetric
or symmetric RBF collocation, or localized RBF or polynomial stencils. This
allows users to compare different discretizations with respect to error bounds
of the above form, without knowing exact solutions, and admitting all possible
ways to set up generalized stiffness matrices. The error analysis is proven to
be sharp under mild additional assumptions. As a byproduct, it allows to
construct worst cases that push discretizations to their limits. All of this is
illustrated by numerical examples.
