
Convergence and consistency analyses 205
The analytical solution derived using the Fourier series is given as T(x,y) =
∑π π−−π π
=
∞
−
Tnnb
xa nya
sn
n
sinh(/)2[1 (1)]sin( /)sinh
1
1
. This problem is
solved, by including up to second order monomials in the shape function basis
and with 5 × 5, 9 × 9, 17 × 17, 21 × 21, 26 × 26, and 33 × 33 eld and 44 × 44
virtual nodes, respectively. The uniform and randomly distributed eld nodes
are combined with the cosine and uniformly distributed virtual nodes. The
convergence rates of both types of virtual nodes are given in Table4.12 and
Table4.13 and corresponding convergence curves are plotted in Fig ...