Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 141-151. 

Title: Issues in adaptive mesh refinement implementation

Authors: Noureddine Hannoun (Univ. of Tennessee, Knoxville, TN, USA)
         Vasilios Alexiades (Univ. of Tennessee, Knoxville, TN, USA)
 
Abstract: 
 Physical phenomena often involve discontinuities and/or localized
 high-gradient areas. The numerical simulation of these problems and
 conventional techniques (Finite Elements, Finite Volumes, Finite
 Differences, and Spectral Methods) with a uniform grid is inefficient
 when high accuracy is required. Adaptive Mesh Refinement (AMR) is a
 technique that allows local refinement of the grid. In this
 presentation, we describe a typical AMR technique and address
 implementation and algorithmic issues. Triangular unstructured grids
 and a regular 1 to 4 refinement are considered.

Published February 28, 2007.
Math Subject Classifications: 68U99, 65M50, 65Y20.
Key Words: Adaptive mesh refinement; data structure; computational method;
           object oriented programming;  conservation laws.