On a superconvergent finite element scheme for elliptic systems. I. Dirichlet boundary condition

Ivan Hlaváček; Michal Křížek

Aplikace matematiky (1987)

  • Volume: 32, Issue: 2, page 131-154
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Hlaváček, 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 -

References

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Citations in EuDML Documents

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  1. Ivan Hlaváček, Michal Křížek, On a superconvergent finite element scheme for elliptic systems. II. Boundary conditions of Newton's or Neumann's type
  2. Wei Chen, Michal Křížek, What is the smallest possible constant in Céa's lemma?
  3. Ivan Hlaváček, Michal Křížek, On a superconvergent finite element scheme for elliptic systems. III. Optimal interior estimates
  4. Balázs Kovács, On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems

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