Solution-Based Mesh Quality Indicators for Triangular and Tetrahedral Meshes

A new mesh quality measure for triangular and tetrahedral meshes is presented. This mesh quality measure is based both on geometrical and solution information and is derived by considering the error when linear triangular and tetrahedral elements are used to approximate a quadratic function. The new measure is shown to be related to existing measures of mesh quality but with the advantage that local solution information in the form of scaled derivatives along edges is taken into account. This advantage is demonstrated by a comparison with a geometrical indicator on a parameterized problem.