A Measure of the Conformity of a Mesh to an Anisotropic Metric

A method is proposed to measure the difference between a give n mesh and the size specification map that this mesh is suppose d to satisfy. The size specification map is given in the form of a Ri emannian metric that specifies both size and stretching of th e mesh to be build. The measure evaluates the difference between th unique metric for which a simplex is a unit equilateral simp lex, and the average value over the simplex of the specified Riemannia n metric. Analytical and numerical examples illustrate the behavior of this measure. This measure is a unique dimensionless numb er that characterizes a whole mesh both in size and in shape, b e it isotropic or anisotropic, coarse or fine, in a small or a big do main, in two or three dimensions.