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We present a comparative numerical study for three functionals used forvariational mesh adaptation. One of them is a generalisation of Winslow'svariable diffusion functional while the others are based on equidistributionand alignment. These functionals are known to have nice theoretical propertiesand work well for most mesh adaptation problems either as a stand-alonevariational method or combined within the moving mesh framework. Theirperformance is investigated numerically in terms of equidistribution andalignment mesh quality measures. Numerical results in 2D and 3D are presented.

A comparative numerical study of meshing functionals for variational mesh adaptation