zbMATH — the first resource for mathematics

A recursive approach to local mesh refinement in two and three dimensions. (English) Zbl 0823.65119
This paper discusses the newest vertex strategy for local refinement in two dimensions. Based on a similar bisection strategy, a recursive algorithm for local refinement of tetrahedral meshes in three dimensions is described. The paper also outlines simple data structures and derefinement algorithms.
Reviewer: Q.Duan (Lafayette)

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Full Text: DOI
[1] Bänsch, E., An adaptive finite-element strategy for the three-dimensional time-dependent navier—stokes equations, J. comput. appl. math., 36, 3-28, (1991) · Zbl 0727.76078
[2] George, P.L., Modulef, (1992), User guide No. 3, INRIA
[3] Mitchell, W.F., Unified multilevel adaptive finite element methods for elliptic problems, Ph.D. thesis, (1988), Dept. Comput. Sci., Univ. Illinois Urbana, IL, Report no. UIUCDCS-R-88-1436
[4] Mitchell, W.F., Adaptive refinement for arbitrary finite-element spaces with hierarchical bases, J. comput. appl. math., 36, 65-78, (1991) · Zbl 0733.65066
[5] Rivara, M.-C., Selective refinement/derefinement algorithms for sequences of nested triangulations, Internat. J. numer. methods engrg., 28, 2889-2906, (1989) · Zbl 0729.65092
[6] Rivara, M.-C., Local modification of meshes for adaptive and/or multigrid finite-element methods, J. comput. appl. math., 36, 79-89, (1991) · Zbl 0733.65075
[7] Sewell, E.G., Automatic generation of triangulation for piecewise polynomial approximation, Ph.D. thesis, (1972), Purdue Univ West Lafayette, IN
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.