Few practical aspects of extending equidistribution principle in higher dimensions: A geometrical insight

It is well known that the equidistribution principle plays a pivotal role in mesh generation to deal with many real world problems which exhibit large solution variations. In one dimension, the principle has been successfully applied and analyzed for various test problems. However, it has been reported in the literature that the equidistribution principle is not sufficient for mesh adaptation in higher dimensions. Yet, most of the commonly used mesh adaptation strategies in higher dimension are directly or indirectly based on equidistibution principle. In this article, we formulate most commonly used mesh adaptation strategies within the framework of equidistribution principle and provide a geometrical insight into the limitations of equidistibution principle for mesh adaptation in higher dimensions, and discuss few possible means to circumvent these limitations.