Local refinement of three-dimensional finite element meshes

Abstract

Mesh refinement is an important tool for editing finite element meshes in order to increase the accuracy of the solution. Refinement is performed in an iterative procedure in which a solution is found, error estimates are calculated, and elements in regions of high error are refined. This process is repeated until the desired accuracy is obtained. Much research has been done on mesh refinement. Research has been focused on two-dimensional meshes and three-dimensional tetrahedral meshes ([1] Ning et al. (1993) Finite Elements in Analysis and Design, 13, 299–318; [2] Rivara, M. (1991) Journal of Computational and Applied Mathematics 36, 79–89; [3] Kallinderis; Vijayar (1993) AIAA Journal,31, 8, 1440–1447; [4] Finite Element Meshes in Analysis and Design,20, 47–70). Some research has been done on three-dimensional hexahedral meshes ([5] Schneiders; Debye (1995) Proceedings IMA Workshop on Modelling, Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations). However, little if any research has been conducted on a refinement algorithm that is general enough to be used with a mesh composed of any three-dimensional element (hexahedra, wedges, pyramids, and/or retrahedra) or any combination of three-dimensional elements (for example, a mesh composed of part hexahedra and part wedges). This paper presents an algorithm for refinement of three-dimensional finite element meshes that is general enough to refine a mesh composed of any combination of the standard three-dimensional element types.