A note on necessary and sufficient conditions for convergence of the finite element method

Kučera, Václav. "A note on necessary and sufficient conditions for convergence of the finite element method." Application of Mathematics 2015. Prague: Institute of Mathematics CAS, 2015. 132-139. <http://eudml.org/doc/287859>.

@inProceedings{Kučera2015,
abstract = {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 $O(h)$ convergence and show a simple relation to classical problems in measure theory and differential geometry which could lead to new insights in the area.},
author = {Kučera, Václav},
booktitle = {Application of Mathematics 2015},
keywords = {finite element method; a priori error estimates; maximum angle condition},
location = {Prague},
pages = {132-139},
publisher = {Institute of Mathematics CAS},
title = {A note on necessary and sufficient conditions for convergence of the finite element method},
url = {http://eudml.org/doc/287859},
year = {2015},
}

TY - CLSWK
AU - Kučera, Václav
TI - A note on necessary and sufficient conditions for convergence of the finite element method
T2 - Application of Mathematics 2015
PY - 2015
CY - Prague
PB - Institute of Mathematics CAS
SP - 132
EP - 139
AB - 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 $O(h)$ convergence and show a simple relation to classical problems in measure theory and differential geometry which could lead to new insights in the area.
KW - finite element method; a priori error estimates; maximum angle condition
UR - http://eudml.org/doc/287859
ER -