Optimal Constrained Interpolation in Mesh-Adaptive Finite Element Modeling

Finite element mesh generation and adaptive meshing

This 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 quadrilat...

Cover interpolation functions and h-enrichment in finite element method

This paper presents a method to improve the generation of meshes and the accuracy of numerical solutions of elasticity problems, in which two techniques of h-refinement and enrichment are used by interpolation cover functions. Initially, regions which possess desired accuracy are detected. Mesh improvment is done through h-refinement for the elements existing in those regions. Total error of th...

An optimal adaptive mixed finite element method

Various applications in fluid dynamics and computational continuum mechanics motivate the development of reliable and efficient adaptive algorithms for mixed finite element methods. In order to save degrees of freedom, not all but just a selection of finite element domains are refined. Hence the fundamental question of convergence as well as the question of optimality require new mathematical a...

An Optimal Adaptive Finite Element Method

Preprint No. 1271, Dept. of Math., Univ. of Utrecht, Submitted to SIAM J. Numer. Anal., March 2003 Although existing adaptive finite element methods for solving second order elliptic equations often perform better in practical computations than non-adaptive ones, usually they are even not proven to converge. Only recently in the works of Dörfler ([Dör96]) and that of Morin, Nochetto and Siebert...

Adaptive Finite Element Methods for Optimal