Computing upper bounds on Friedrichs’ constant

Vejchodský, Tomáš. "Computing upper bounds on Friedrichs’ constant." Applications of Mathematics 2012. Prague: Institute of Mathematics AS CR, 2012. 278-289. <http://eudml.org/doc/287829>.

@inProceedings{Vejchodský2012,
abstract = {This contribution shows how to compute upper bounds of the optimal constant in Friedrichs’ and similar inequalities. The approach is based on the method of $a priori-a posteriori inequalities$ [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs’ constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed upper bound on Friedrichs’ constant in a posteriori error estimation to obtain guaranteed error bounds.},
author = {Vejchodský, Tomáš},
booktitle = {Applications of Mathematics 2012},
keywords = {second-order boundary value problems; a posteriori error estimates; complementary energy; Friedrichs’ inequality; numerical example},
location = {Prague},
pages = {278-289},
publisher = {Institute of Mathematics AS CR},
title = {Computing upper bounds on Friedrichs’ constant},
url = {http://eudml.org/doc/287829},
year = {2012},
}

TY - CLSWK
AU - Vejchodský, Tomáš
TI - Computing upper bounds on Friedrichs’ constant
T2 - Applications of Mathematics 2012
PY - 2012
CY - Prague
PB - Institute of Mathematics AS CR
SP - 278
EP - 289
AB - This contribution shows how to compute upper bounds of the optimal constant in Friedrichs’ and similar inequalities. The approach is based on the method of $a priori-a posteriori inequalities$ [9]. However, this method requires trial and test functions with continuous second derivatives. We show how to avoid this requirement and how to compute the bounds on Friedrichs’ constant using standard finite element methods. This approach is quite general and allows variable coefficients and mixed boundary conditions. We use the computed upper bound on Friedrichs’ constant in a posteriori error estimation to obtain guaranteed error bounds.
KW - second-order boundary value problems; a posteriori error estimates; complementary energy; Friedrichs’ inequality; numerical example
UR - http://eudml.org/doc/287829
ER -