TY - JOUR
T1 - A Mesh Adaptation Method for 1D-Boundary Layer Problems
JO - International Journal of Numerical Analysis Modeling Series B
VL - 4
SP - 408
EP - 428
PY - 2012
DA - 2012/03
SN - 3
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnamb/292.html
KW - hierarchical error estimation
KW - mesh adaptation
KW - singular perturbation
KW - boundary layer problems
AB - 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.