Abstract
This article considered the traditional finite element method (FEM) and adaptive finite element method (FEM) for the numerical solution of the one-dimensional boundary value problems. We established the preference or the superiority of the h-adaptive FEM to traditional FEM in high gradient problems in terms of accuracy and cost of computation. Numerical examples which confirm the performance and adaptability of the h-adaptive method over the traditional finite element method and the high accuracy of the numerical solution are presented. Detailed error analysis of linear elements was also discussed. In conclusion, h-adaptive FEM is recommended for complex systems with high gradient problems.
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