In this short note, we present several ideas and observations concerning finite element convergence and the role of the maximum angle condition. Based on previous work, we formulate a hypothesis concerning a necessary condition for $O\left(h\right)$ convergence and show a simple relation to classical problems in measure theory and differential geometry which could lead to new insights in the area.

EUDML-ID : urn:eudml:doc:287859
Mots clés:
Mots clés:

@article{702971,
     title = {A note on necessary and sufficient conditions for convergence of the finite element method},
     booktitle = {Application of Mathematics 2015},
     series = {GDML\_Books},
     publisher = {Institute of Mathematics CAS},
     address = {Prague},
     year = {2015},
     pages = {132-139},
     zbl = {06669925},
     url = {http://dml.mathdoc.fr/item/702971}
}

Kučera, Václav. A note on necessary and sufficient conditions for convergence of the finite element method, dans Application of Mathematics 2015, GDML_Books,  (2015), pp. 132-139. http://gdmltest.u-ga.fr/item/702971/