We investigate the application of a multiscale sparse grid finite element method for computing numerical solutions to a two-dimensional singularly perturbed convection-diffusion problem posed on the unit square. Typically, sparse grid methods are constructed using a hierarchical basis (see, e.g., Bungartz and Griebel [1]). In our approach, the method is presented as a generalisation of the two-scale method described in Liu et al. [3], and is related to the combination technique outlined by Pflaum and Zhou [7]. We show that this method retains the same level of accuracy, in the energy norm, as both the standard Galerkin and two-scale methods. The computational cost associated with the method, however, is $\mathcal{O}(N \log N)$, compared to $\mathcal{O}(N^2)$ and $\mathcal{O}(N^{3/2})$ for the Galerkin and two-scale methods respectively.

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