Uniform
O
(
h
2
)
\mathcal {O}({h^2})
convergence is proved for the El-Mistikawy-Werle discretization of the problem
−
ε
u
+
a
u
′
+
b
u
=
f
- \varepsilon u+ au’+ bu = f
on (0,1),
u
(
0
)
=
A
u(0) = A
,
u
(
1
)
=
B
u(1) = B
, subject only to the conditions
a
,
b
,
f
∈
W
2
,
∞
[
0
,
1
]
a,b,f \in {\mathcal {W}^{2,\infty }}[0,1]
and
a
(
x
)
>
0
,
0
≤
x
≤
1
a(x) > 0, 0 \leq x \leq 1
. The principal tools used are a certain representation result for the solutions of such problems that is due to the author [Math. Comp., v. 48, 1987, pp. 551-564] and the general stability results of Niederdrenk and Yserentant [Numer. Math., v. 41, 1983, pp. 223-253]. Global uniform
O
(
h
)
\mathcal {O}(h)
convergence is proved under slightly weaker assumptions for an equivalent Petrov-Galerkin formulation.