Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems

Jim Douglas Jr., et al. "Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 747-770. <http://eudml.org/doc/197573>.

@article{JimDouglasJr2010,
abstract = { Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω) and in the Neumann and Robin cases in L2(Ω). },
author = {Jim Douglas Jr., Santos, Juan E., Sheen, Dongwoo, Ye, Xiu},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonconforming Galerkin methods; quadrilateral elements; second order elliptic problems; domain decomposition iterative methods.; domain decomposition; iterative methods; nonconforming Galerkin methods; second order elliptic equations; error estimates},
language = {eng},
month = {3},
number = {4},
pages = {747-770},
publisher = {EDP Sciences},
title = {Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems},
url = {http://eudml.org/doc/197573},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Jim Douglas Jr.
AU - Santos, Juan E.
AU - Sheen, Dongwoo
AU - Ye, Xiu
TI - Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4
SP - 747
EP - 770
AB - Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be based on P1, as for conforming elements; however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in H1(Ω) and in the Neumann and Robin cases in L2(Ω).
LA - eng
KW - Nonconforming Galerkin methods; quadrilateral elements; second order elliptic problems; domain decomposition iterative methods.; domain decomposition; iterative methods; nonconforming Galerkin methods; second order elliptic equations; error estimates
UR - http://eudml.org/doc/197573
ER -