A Check of Mesh Quality

Even if a mesh is valid and all of the elements are approximately the same size, the quality, as measured by parameters such as aspect ratio, skew, and Jacobian quality metrics, may be poor. Theoretically, the FE solution should approach the exact solution as the size of the largest element approaches zero. It has been demonstrated, however, that if dihedral angles approach π as the element size decreases, convergence to the exact solution may fail. ABAQUS, for example, checks the distortion of each element through the angle between isoparametric lines of each element. In general, the criterion set for this test consists of verifying whether the angle is greater than 45o or less than 135o in order to reduce the influence of the element distortion on the accuracy of the numerical integration.