On exact results in the finite element method

Ivan Hlaváček; Michal Křížek

Applications of Mathematics (2001)

  • Volume: 46, Issue: 6, page 467-478
  • ISSN: 0862-7940

Abstract

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We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution u . We show that the Galerkin approximation of u based on the so-called biharmonic finite elements is independent of the values of u in the interior of any subelement.

How to cite

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Hlaváček, Ivan, and Křížek, Michal. "On exact results in the finite element method." Applications of Mathematics 46.6 (2001): 467-478. <http://eudml.org/doc/33097>.

@article{Hlaváček2001,
abstract = {We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution $u$. We show that the Galerkin approximation of $u$ based on the so-called biharmonic finite elements is independent of the values of $u$ in the interior of any subelement.},
author = {Hlaváček, Ivan, Křížek, Michal},
journal = {Applications of Mathematics},
keywords = {boundary value elliptic problems; finite element method; generalized splines; elastic plate; elliptic boundary value problems; finite element method; numerical example; Galerkin method; biharmonic problem},
language = {eng},
number = {6},
pages = {467-478},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On exact results in the finite element method},
url = {http://eudml.org/doc/33097},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Hlaváček, Ivan
AU - Křížek, Michal
TI - On exact results in the finite element method
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 6
SP - 467
EP - 478
AB - We prove that the finite element method for one-dimensional problems yields no discretization error at nodal points provided the shape functions are appropriately chosen. Then we consider a biharmonic problem with mixed boundary conditions and the weak solution $u$. We show that the Galerkin approximation of $u$ based on the so-called biharmonic finite elements is independent of the values of $u$ in the interior of any subelement.
LA - eng
KW - boundary value elliptic problems; finite element method; generalized splines; elastic plate; elliptic boundary value problems; finite element method; numerical example; Galerkin method; biharmonic problem
UR - http://eudml.org/doc/33097
ER -

References

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