Approximation of conservative fields and the element 'edge shape matrix'

The accuracy of finite element approximation on tetrahedral elements is studied using the previously derived maximum eigenvalue condition. This condition is linked with the minimum singular value of the element 'edge shape matrix' that characterizes the flatness of an element. A geometric interpretation of these results is discussed. From the theoretical viewpoint, a better insight into the mechanism of approximation errors is gained. From the practical perspective, a precise characterization of shape of tetrahedral elements becomes possible.