A Mesh Adaptation Method for 1d-boundary Layer Problems

We present a one-dimensional version of a general mesh adaptation technique developed in [1, 2] which is valid for two and three-dimensional problems. The simplicity of the one-dimensional case allows to detail all the necessary steps with very simple computations. We show how the error can be estimated on a piecewise finite element of degree k and how this information can be used to modify the grid using local mesh operations: element division, node elimination and node displacement. Finally, we apply the whole strategy to many challenging singularly perturbed boundary value problems where the one-dimensional setting allows to push the adaptation method to its limits.