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.
Similar content being viewed by others
References
Ning; Yu-Wei; Suprobo, P.; Jeong, G.D.; Ting, E.C. (1993) A regional mixed refinement procedure for finite element mesh design. Finite Elements in Analysis and Design, 13, 299–318
Rivara, M. (1991) Local modifications of meshes for adaptive and/or multigrid finite-element methods. Journal of Computational and Applied Mathematics, 36, 79–89
Kallinderis, Y.; Vijayan, P. (1993) Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes. AIAA Journal, 31, 8, 1440–1447
Lewis, R.W.; Zheng, Y.; Usmani, A.S. (1995) Aspects of adaptive mesh generation based on domain decomposition and Delaunay triangulation. Finite Element Meshes in Analysis and Design, 20, 47–70
Schneiders, R.; Debye, J. (1995) Refinement algorithms for unstructured quadrilateral or brick element meshes. Proceedings IMA Workshop on Modeling, Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations
Staten, M.L. (1996) Selective refinement of two and three-dimensional finite element meshes, Master's Thesis, Brigham Young University, April 1996, http://www.et.byu/≈geos/refine.html
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Staten, M.L., Jones, N.L. Local refinement of three-dimensional finite element meshes. Engineering with Computers 13, 165–174 (1997). https://doi.org/10.1007/BF01221213
Issue Date:
DOI: https://doi.org/10.1007/BF01221213