On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
Aplikace matematiky (1987)
- Volume: 32, Issue: 2, page 131-154
- ISSN: 0862-7940
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topHlaváček, Ivan, and Křížek, Michal. "On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition." Aplikace matematiky 32.2 (1987): 131-154. <http://eudml.org/doc/15485>.
@article{Hlaváček1987,
abstract = {Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate $O(h^\{3/2\})$ is proved in the $L^2$-norm. For a class of polygonal domains the global estimate $O(h^2)$ can be proven.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Aplikace matematiky},
keywords = {post-processing; averaged gradient; Galerkin method; system; finite elements; superconvergence; global estimate; elliptic systems; post-processing; averaged gradient; Galerkin method; system; finite elements; superconvergence; global estimate},
language = {eng},
number = {2},
pages = {131-154},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition},
url = {http://eudml.org/doc/15485},
volume = {32},
year = {1987},
}
TY - JOUR
AU - Hlaváček, Ivan
AU - Křížek, Michal
TI - On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 2
SP - 131
EP - 154
AB - Second order elliptic systems with Dirichlet boundary conditions are solved by means of affine finite elements on regular uniform triangulations. A simple averagign scheme is proposed, which implies a superconvergence of the gradient. For domains with enough smooth boundary, a global estimate $O(h^{3/2})$ is proved in the $L^2$-norm. For a class of polygonal domains the global estimate $O(h^2)$ can be proven.
LA - eng
KW - post-processing; averaged gradient; Galerkin method; system; finite elements; superconvergence; global estimate; elliptic systems; post-processing; averaged gradient; Galerkin method; system; finite elements; superconvergence; global estimate
UR - http://eudml.org/doc/15485
ER -
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Citations in EuDML Documents
top- Ivan Hlaváček, Michal Křížek, On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
- Ivan Hlaváček, Michal Křížek, On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
- Wei Chen, Michal Křížek, What is the smallest possible constant in Céa's lemma?
- Balázs Kovács, On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems
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