  We developed the theory of finite volume form factors in the presence of
integrable defects. These finite volume form factors are expressed in terms of
the infinite volume form factors and the finite volume density of states and
incorporate all polynomial corrections in the inverse of the volume. We tested
our results, in the defect Lee-Yang model, against numerical data obtained by
truncated conformal space approach (TCSA), which we improved by renormalization
group methods adopted to the defect case. To perform these checks we determined
the infinite volume defect form factors in the Lee-Yang model exactly,
including their vacuum expectation values. We used these data to calculate the
two point functions, which we compared, at short distance, to defect CFT. We
also derived explicit expressions for the exact finite volume one point
functions, which we checked numerically. In all of these comparisons excellent
agreement was found.
