We report on implementing curved elements (CEs) into the discontinuous Galerkin (DG) method in order to improve the nano-optical simulation of realistic nanostructures. Compared to straight meshes, CEs as realized here by triangles with one bent side allow for a faster, more accurate and robust computation. Clearly, CEs much better match real physical nanostructures, where surface energies, tension and adhesion give rise to rounded geometries rather than planar surfaces. The novel code was tested by calculating the spatial field distributions and scattering cross sections for two-dimensional (2D) nano-objects, namely a nanosphere and a V-groove. When using a fixed mesh size, we found that CEs much more accurately describe the curved geometries than ordinary linear elements, leading to significantly smaller errors. Moreover, CEs turned out to be between 2.5 and 37 times faster for the same error margin and to be more robust against unphysical behavior, such as hot spots at element vertices or unmotivated spectral features. Integrating CEs into the DG algorithm thus constitutes an excellent choice for numerical modeling of complex problems- especially in the context of plasmonics.