With bim 1.1.4 and octave 3.8.1 on Debian, I get the following:

octave:1> test bim2a_axisymmetric_advection_diffusion
  ***** test
 n         = 3;
 [mesh]    = msh2m_structured_mesh(linspace(-2,-1,n+1),linspace(0,1,n+1),1,1:4);
 mesh      = bim2c_mesh_properties(mesh);
 uex       = @(r,z) exp(r);
 duexdr    = @(r,z) uex(r,z);
 d2uexdr2  = @(r,z) uex(r,z);
 duexdz    = @(r,z) 0*uex(r,z);
 d2uexdz2  = @(r,z) 0*uex(r,z);
 Dnodes    = bim2c_unknowns_on_side(mesh,[2,4]);
 Nnodes    = columns(mesh.p);
 Nelements = columns(mesh.t);
 Varnodes  = setdiff(1:Nnodes,Dnodes);
 D = 1; vr = 1; vz = 0;
 alpha     = D*ones(Nelements,1);
 gamma     = ones(Nnodes,1);
 eta       = ones(Nnodes,1);
 beta      = 1/D*[vr*ones(1,Nelements); vz*ones(1,Nelements)];
 f = @(r,z) -D./r.*duexdr(r,z) - D.*d2uexdr2(r,z) ...
           + vr./r .* uex(r,z) + vr * duexdr(r,z) ...
           - D.*d2uexdz2(r,z) + vz * duexdz(r,z);
 rhs = bim2a_axisymmetric_rhs(mesh, ones(Nelements,1), f(mesh.p(1,:), mesh.p(2,:)));
 S   = bim2a_axisymmetric_advection_diffusion(mesh,alpha,gamma,eta,beta);
 u   = zeros(Nnodes,1); u(Dnodes) = uex(mesh.p(1,Dnodes), mesh.p(2,Dnodes));
 u(Varnodes) = S(Varnodes,Varnodes)\(rhs(Varnodes) - S(Varnodes,Dnodes)*u(Dnodes));
 assert(u,uex(mesh.p(1,:), mesh.p(2,:))',1e-7)
!!!!! test failed
ASSERT errors for:  assert (u,uex (mesh.p (1, :), mesh.p (2, :))',1e-7)

  Location  |  Observed  |  Expected  |  Reason
    (5)        0.20395      0.18888      Abs err 0.015075 exceeds tol 1e-07
    (6)        0.20429      0.18888      Abs err 0.015412 exceeds tol 1e-07
    (7)        0.20453      0.18888      Abs err 0.015655 exceeds tol 1e-07
    (8)        0.20486      0.18888      Abs err 0.015987 exceeds tol 1e-07
    (9)        0.27714       0.2636      Abs err 0.013543 exceeds tol 1e-07
    (10)       0.27763       0.2636      Abs err 0.014036 exceeds tol 1e-07
    (11)       0.27793       0.2636      Abs err 0.014331 exceeds tol 1e-07
    (12)        0.2784       0.2636      Abs err 0.014808 exceeds tol 1e-07