On the quality of local flux reconstructions for guaranteed error bounds

Vejchodský, Tomáš. "On the quality of local flux reconstructions for guaranteed error bounds." Application of Mathematics 2015. Prague: Institute of Mathematics CAS, 2015. 242-255. <http://eudml.org/doc/287836>.

@inProceedings{Vejchodský2015,
abstract = {In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate the efficiency of these flux reconstructions by their comparison with the optimal flux reconstruction computed as a global minimization problem.},
author = {Vejchodský, Tomáš},
booktitle = {Application of Mathematics 2015},
keywords = {a posteriori error estimates; complementarity; index of effectivity; elliptic problem; reaction-diffusion; singular perturbation},
location = {Prague},
pages = {242-255},
publisher = {Institute of Mathematics CAS},
title = {On the quality of local flux reconstructions for guaranteed error bounds},
url = {http://eudml.org/doc/287836},
year = {2015},
}

TY - CLSWK
AU - Vejchodský, Tomáš
TI - On the quality of local flux reconstructions for guaranteed error bounds
T2 - Application of Mathematics 2015
PY - 2015
CY - Prague
PB - Institute of Mathematics CAS
SP - 242
EP - 255
AB - In this contribution we consider elliptic problems of a reaction-diffusion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodsky [2] and the reconstruction of Braess and Schöberl [5]. We evaluate the efficiency of these flux reconstructions by their comparison with the optimal flux reconstruction computed as a global minimization problem.
KW - a posteriori error estimates; complementarity; index of effectivity; elliptic problem; reaction-diffusion; singular perturbation
UR - http://eudml.org/doc/287836
ER -