Finite element mesh generation and adaptive meshing

Abstract

AbstractThis review paper gives a detailed account of the development of mesh generation techniques on planar regions, over curved surfaces and within volumes for the past years. Emphasis will be on the generation of the unstructured meshes for purpose of complex industrial applications and adaptive refinement finite element analysis. Over planar domains and on curved surfaces, triangular and quadrilateral elements will be used, whereas for three‐dimensional structures, tetrahedral and hexahedral elements have to be generated. Recent advances indicate that mesh generation on curved surfaces is quite mature now that elements following closely to surface curvatures could be generated more or less in an automatic manner. As the boundary recovery procedure are getting more and more robust and efficient, discretization of complex solid objects into tetrahedra by means of Delaunay triangulation and other techniques becomes routine work in industrial applications. However, the decomposition of a general object into hexahedral elements in a robust and efficient manner remains as a challenge for researchers in the mesh generation community. Algorithms for the generation of anisotropic meshes on 2D and 3D domains have also been proposed for problems where elongated elements along certain directions are required. A web‐site for the latest development in meshing techniques is included for the interested readers.