Finite Elements in Analysis and Design 31 (1998) 33 — 53 Geometric evaluation of finite element surface meshes Pascal J. Frey*, Houman Borouchaki INRIA, projet Gamma, Domaine de Voluceau-Rocquencourt, 78153 Le Chesnay cedex, France UTT, GSM-LASMIS, 12 rue Marie Curie, 10010 Troyes cedex, France Abstract This paper presents several general-purpose criteria for evaluating finite element surface meshes. These criteria are exclusively based on geometric feature analysis. Theoretical aspects are described and a geometric interpretation of each criterion is provided. The evaluation of surface meshes for finite element methods is discussed and several application examples are presented to justify the introduction of the proposed criteria. 1998 Elsevier Science B.V. All rights reserved. Keywords: Surface triangulation; Mesh quality; Piecewise planar surface approximation 1. Introduction Surface triangulations are commonly used in a wide range of applications (e.g. computer graphics, numerical simulations, etc.). For finite element methods however, the quality of the geometric approximation (i.e., the discretization of the domain boundaries) is of significant importance because of its effect on the accuracy of the numerical solutions and the convergence of the computational scheme. In this context, a finite element surface mesh is intended to be the boundary description for a three-dimensional finite element analysis. Therefore, a surface mesh must be an optimal piecewise planar approximation of the original surface such that the maximal distance between the original and the approximating surface does not exceed a given tolerance. Moreover, a surface mesh represents a valid approximation of the underlying surface if the shapes of the elements are optimal with respect to the convergence of the computational scheme and the * Corresponding author. E-mail: pascal.frey@inria.fr. Assuming that the discrete solution converges toward the exact solution. 0168-874X/98/$ — see front matter 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 8 7 4 X ( 9 8 ) 0 0 0 4 6 - 8