@Article{IJNAM-16-499, author = {Becher , Simon}, title = {FEM-Analysis on Graded Meshes for Turning Point Problems Exhibiting an Interior Layer}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {16}, number = {3}, pages = {499--518}, abstract = {

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$2-norm on these graded meshes.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/12879.html} }