TY - JOUR
T1 - FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer
AU - Becher , Simon
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 499
EP - 518
PY - 2018
DA - 2018/11
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/12879.html
KW - Singular perturbation, turning point, interior layer, layer-adapted meshes, higher order finite elements.
AB - <p style="text-align: justify;">We consider singularly perturbed boundary value problems with a simple interior turning
point whose solutions exhibit an interior layer. These problems are discretised using higher order finite
elements on layer-adapted graded meshes proposed by Liseikin. We prove $ε$-uniform error estimates
in the energy norm. Furthermore, for linear elements we are able to prove optimal order $ε$-uniform
convergence in the $L$<sup>2</sup>-norm on these graded meshes.</p>