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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 [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.
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 -