Voir la notice de l'article provenant de la source Numdam
A class of compatible spatial discretizations for solving partial differential equations is presented. A discrete exact sequence framework is developed to classify these methods which include the mimetic and the covolume methods as well as certain low-order finite element methods. This construction ensures discrete analogs of the differential operators that satisfy the identities and theorems of vector calculus, in particular a Helmholtz decomposition theorem for the discrete function spaces. This paper demonstrates that these methods differ only in their choice of discrete inner product. Finally, certain uniqueness results for the covolume inner product are shown.
@article{M2AN_2008__42_6_941_0,
author = {Trapp, Kathryn A.},
title = {Inner products in covolume and mimetic methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {941--959},
publisher = {EDP-Sciences},
volume = {42},
number = {6},
year = {2008},
doi = {10.1051/m2an:2008030},
mrnumber = {2473315},
zbl = {1155.65103},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008030/}
}
TY - JOUR AU - Trapp, Kathryn A. TI - Inner products in covolume and mimetic methods JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2008 SP - 941 EP - 959 VL - 42 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008030/ DO - 10.1051/m2an:2008030 LA - en ID - M2AN_2008__42_6_941_0 ER -
%0 Journal Article %A Trapp, Kathryn A. %T Inner products in covolume and mimetic methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2008 %P 941-959 %V 42 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008030/ %R 10.1051/m2an:2008030 %G en %F M2AN_2008__42_6_941_0
Trapp, Kathryn A. Inner products in covolume and mimetic methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 42 (2008) no. 6, pp. 941-959. doi: 10.1051/m2an:2008030
Cité par Sources :