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• Unified least-squares-based framework for fast "nodal" and "element" strategies of mapping scalar CT voxel densities onto finite element mesh. • Approximation of density by finite element method using least squares projection. • The discontinuous variant of the finite element method is more suitable for density approximation than the continuous variant in terms of accuracy and efficiency. • The discontinuous zero-order finite element method preserves the density spectrum better than the continuous one. The spatially varying mechanical properties in finite element models of bone are most often derived from bone density data obtained via quantitative computed tomography. The key step is to accurately and efficiently map the density given in voxels to the finite element mesh. The density projection is first formulated in least-squares terms and then discretized using a continuous and discontinuous variant of the finite element method. Both discretization variants are compared with the nodal and element approaches known from the literature. In terms of accuracy in the L2 norm, energy distance and efficiency, the discontinuous zero-order variant appears to be the most advantageous. The proposed variant sufficiently preserves the spectrum of density at the edges, while keeping computational cost low. The continuous finite element method is analogous to the nodal formulation in the literature, while the discontinuous finite element method is analogous to the element formulation. The two variants differ in terms of implementation, computational cost and ability to preserve the density spectrum. These differences cannot be described and measured by known indirect methods from the literature. [ABSTRACT FROM AUTHOR]