Associated primes of local cohomology after adjoining indeterminates

Let A be a domain finitely generated as an algebra over a field, k  , of characteristic zero, R=A[t1,…,tn]R=A[t1,…,tn] or A[[t1,…,tn]]A[[t1,…,tn]] and I⊂RI⊂R any ideal. If A   has a resolution of singularities, Y0Y0, which is the blowup of A   along an ideal of depth at least two and is covered by either two or three open affines with Hj(Y0,OY0)Hj(Y0,OY0) of finite length over A   for j>0j>0, we prove that AssRHIi(R) is finite for every i. In particular this holds when A is a two or three dimensional normal domain with an isolated singularity which is finitely generated over a field of characteristic 0.