Anisotropic Mesh Refinement Research Articles

3D anisotropic mesh refinement in compliance with a general metric specification

A simple and efficient anisotropic refinement procedure for the three-dimensional tetrahedral element mesh based on successive bisection of edges is proposed. Refinement is done by dividing lines of the mesh based on the lengths calculated on three points as specified by the metric tensor along the direction of the line. To obtain the best mesh quality, the subdivision of line segments is performed in the sequence according to the length of the line segments to be divided. Such an order of priority can be determined by a simple sorting process on all the line segments for which refinement is needed. This list of ordered line segments has to be updated from time to time to take into account the new line segments generated during the subdivision process. From the examples studied, the CPU time for mesh refinement seems to bear a linear relationship with the number of elements generated, with a refinement rate of up to 30 000 elements/s on an IBM Power Station 3BT. Shape optimization procedures can be applied to the refined mesh to further improve the quality of the elements. The refinement scheme is useful as part of a general three-dimensional mesh generation package, or as the mesh refinement module in an adaptive finite element analysis.

Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems

We consider the numerical approximation of a singularly perturbed reaction-diffusion problem over a square. Two different approaches are compared namely: adaptive isotropic mesh refinement and anisotropic mesh refinement. Thus, we compare the h-refinement and the Shishkin mesh approaches numerically with PLTMG software [1]. It is shown how isotropic elements lead to over-refinement and how anisotropic mesh refinement is much more efficient in thin boundary layers.

Anisotropic mesh refinement for problems with internal and boundary layers

Anisotropic mesh refinement for problems with internal and boundary layers

Anisotropic mesh refinement for problems with internal and boundary layers

The character of convection-dominated, singularly perturbed boundary value problems requires their special numerical treatment in order to guarantee stability and resolve existing layers with acceptable accuracy. In addition to discretization methods particularly developed for this aim, recently more and more attention has been directed towards adapted triangulations of the computational domain. In this paper, an adaptive strategy based on an anisotropic refinement is developed for finite element methods. Starting from some a priori information about the location of layers, the so-called hybrid meshes are constructed. By these meshes, the flexibility of unstructured meshes, good approximation properties in layers, and relatively simple rules for a posteriori anisotropic refinement are combined with each other. The efficiency of this procedure is demonstrated by selected numerical examples. Copyright © 1999 John Wiley & Sons, Ltd.

Anisotropic mesh refinement in stabilized Galerkin methods

The numerical solution of a convection-diffusion-reaction model problem is considered in two and three dimensions. A stabilized finite element method of Galerkin/Least-square type accomodates diffusion-dominated as well as convection- and/or reaction-dominated situations. The resolution of boundary layers occuring in the singularly perturbed case is achieved using anisotropic mesh refinement in boundary layer regions. In this paper, the standard analysis of the stabilized Galerkin method on isotropic meshes is extended to more general meshes with boundary layer refinement. Simplicial Lagrangian elements of arbitrary order are used.

An anisotropic h-type mesh-refinement strategy

An anisotropic h-type mesh refinement strategy for finite element approximations is presented. The strategy consists of subsecting quadrilateral elements in one of two possible directions. The decision which elements should be subsected and in which direction is based on minimization of interpolation errors. The method is especially suitable for approximate solutions which in some regions display almost one-dimensional behavior, for instance solutions with boundary layers.