An r-Adaptive Technique for Unstructured Grids Based on the Segment Spring Analogy Method

Abstract

A simple and effective r-adaptive technique for unstructured grids based on the segment spring analogy method is proposed. The finite element method and a corresponding error estimate method using second derivatives are used for computation. The traditional segment spring analogy method is modified, based on an idea of controlling the equilibrium length of the fictitious springs, and used for mesh adjustment. The principle of making numerical errors distributed uniformly over all elements is applied. Three numerical examples involving the one-dimensional (1D) convection-diffusion equation, the two-dimensional (2D) linear parabolic equation and the 2D Euler equations are presented and the effectiveness of the proposed r-type grid adaptive technique is examined.