TY - JOUR
T1 - Lower a posteriori error estimates on anisotropic meshes
AU - Kopteva, Natalia
N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper (Kopteva in Numer Math 137:607–642, 2017) is efficient on partially structured anisotropic meshes.
AB - Lower a posteriori error bounds obtained using the standard bubble function approach are reviewed in the context of anisotropic meshes. A numerical example is given that clearly demonstrates that the short-edge jump residual terms in such bounds are not sharp. Hence, for linear finite element approximations of the Laplace equation in polygonal domains, a new approach is employed to obtain essentially sharper lower a posteriori error bounds and thus to show that the upper error estimator in the recent paper (Kopteva in Numer Math 137:607–642, 2017) is efficient on partially structured anisotropic meshes.
KW - Anisotropic triangulation
KW - Estimator efficiency
KW - Lower a posteriori error estimate
UR - http://www.scopus.com/inward/record.url?scp=85088790608&partnerID=8YFLogxK
U2 - 10.1007/s00211-020-01137-9
DO - 10.1007/s00211-020-01137-9
M3 - Article
AN - SCOPUS:85088790608
SN - 0029-599X
VL - 146
SP - 159
EP - 179
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 1
ER -