# Adaptive solver: re-mesh strategy in 2D

## Introduction

In the process of adaptive solving, it is essential to determine a threshold that will include the meshing areas to be refined. This threshold depends primarily on the number of finite elements of the considered region. Two cases are then considered:

- A number of elements less than, or equal with 100
- A number of elements greater than 100

## Sparse number of finite elements

In the first case, the number of finite elements is considered too sparse to establish a statistical law. The selection threshold is then defined in a controlled manner. Correspondingly, this threshold diminishes with the number of elements.

## High number of finite elements

In the second case, the repartition of the number of finite elements is observed as a function of the size order of the error criterion. This permits the establishment of a logarithmic distribution law. The Gaussian law, thus obtained, is compared with the Gaussian law centered over the same interval. This allows the adjustment of the selection threshold. Thus, it depends both on the repartition and on the number of elements.