Erratum to: J Sci Comput DOI 10.1007/s10915-011-9570-7

1. Equation (24) should change to

$$ \frac{\partial u }{ \partial x_{m} } \biggm{|}_{x_m(0)} = \lim_{\varepsilon \rightarrow 0} \frac{ u( x_{m} (\varepsilon) ) - u( x_{m} (- \varepsilon) ) }{ x_{m} (\varepsilon) + x_{m} (-\varepsilon)} $$
(24)

and consequently equation (27) should change to

$$ \frac{\partial u}{\partial y_m} \biggm{|}_{x_m(0)} \le \frac{ u( \xi^{i+1}_m ) - u(\xi^{i-1}_m) }{ h^i_m + h^{i-1}_m } + \frac{1}{2} \bigl\| u'' ( \xi^i_m ) \bigr\| \biggl( \frac{h_m^3}{R^2} \biggr). $$
(27)

2. Equation (33) should change to

$$ \biggl\| \frac{\partial u}{\partial \xi_m} - \frac{\partial u}{\partial y_m} \biggr\| \le \sum_{j=1}^2 \sum_{k=1}^3 \biggl\| \frac{\partial s_j}{\partial z_k} \frac{\partial z_k}{\partial \xi_m} \biggr\| \biggl\| \frac{\partial u^e}{\partial s_j} - \frac{\partial u}{\partial s_j} \biggr\| $$
(33)

and accordingly in the last line of the proof.

3. In Proposition 4, “the exponential error for the Galerkin scheme…” should be changed to “the MMF error for the Galerkin scheme”.

4. In Proposition 5, “…the MMF error to be negligible compared to the differentiation error in the MMF scheme” should be changed to “…the MMF error to be negligible compared to the differentiation error in the Galerkin scheme”.