Title:         Tetrahedral bisection and adaptive finite elements

Authors:       Douglas N. Arnold and Arup Mukherjee

Source:        in: "Grid Generation and Adaptive Algorithms" (M. Bern, J. E. Flaherty,
and M. Luskin, eds.), IMA Volumes in Mathematics and its Applications 113,
Springer-Verlag, New York-Heidelberg-Berlin, 1999, pp. 29-42

Status:        Published

Abstract:       An adaptive finite element algorithm for elliptic
boundary value problems in $\R^3$ is presented. The algorithm uses
linear finite elements, a-posteriori error estimators, a mesh
refinement scheme based on bisection of tetrahedra, and a multi-grid
solver. We show that the repeated bisection of an arbitrary tetrahedron
leads to only a finite number of dissimilar tetrahedra, and that the
recursive algorithm ensuring conformity of the meshes produced
terminates in a finite number of steps. A procedure for assigning
numbers to tetrahedra in a mesh based on a-posteriori error estimates,
indicating the degree of refinement of the tetrahedron, is also
presented. Numerical examples illustrating the effectiveness of the
algorithm are given.

Keywords:      finite elements, adaptive mesh refinement, error estimators, bisection of tetrahedra

Subj. class.:  65N50

URL:           http://ima.umn.edu/~arnold/papers/bistetima.pdf