Given a differential equation that admits a group of symmetries, it is frequently desirable to preserve those symmetries when constructing a numerical scheme. For solutions that exhibit sharp variations or singularities, symmetry-preserving numerical schemes have proven to give very good numerical results. In the last 25 years, most of the research in this field has focused on the construction of symmetry-preserving finite difference numerical schemes. Extending known results to other types of numerical methods (such as finite element, finite volume, or spectral methods) remains a challenge. In this talk, I will report on preliminary results related to the construction of symmetry-preserving finite element numerical schemes. This is a joint work with Professor Alexander Bihlo from Memorial University.