Measuring the conformity of non-simplicial elements to an anisotropic metric field

This paper extends an approach for measuring the element conformity of simplices to non-simplicial elements of any type, in spaces of arbitrary dimension. Element non-conformity is defined as the difference between a given size specification map, in the form of a Riemannian metric tensor, and the actual metric tensor of the element. An approach to the measurement of non-conformity coefficients of non-simplicial elements based on sub-simplex division is proposed. An analysis of the measure’s behaviour presented for quadrilaterals, hexahedra, prisms and pyramids shows that the measure is sensitive to size, stretching and orientation variations, as well as to other types of element shape degeneration. Finally, numerical applications show that the metric conformity measure can be used as a quality measure to quantify the discrepancy between a whole non-simplicial mesh and a complex anisotropic size specification map.