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TETRAHEDRAL BISECTION AND ADAPTIVE FINITE DOUGLAS N. ARNOLD AND ARUP MUKHERJEE
 

Summary: TETRAHEDRAL BISECTION AND ADAPTIVE FINITE
ELEMENTS
DOUGLAS N. ARNOLD AND ARUP MUKHERJEE
Abstract. An adaptive finite element algorithm for elliptic boundary value prob-
lems in R3 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 con-
formity 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, indicat-
ing the degree of refinement of the tetrahedron, is also presented. Numerical examples
illustrating the effectiveness of the algorithm are given.
Key words. finite elements, adaptive mesh refinement, error estimators, bisection
of tetrahedra
AMS(MOS) subject classifications. 65N50.
1. Introduction. In this article, we describe an algorithm for the
accurate and efficient computation of solutions to elliptic boundary value
problems in R3
. The algorithm creates a sequence of adapted tetrahedral
meshes starting form an initial coarse tetrahedral mesh, and the solution is

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics