A finite element convergence analysis for 3D Stokes equations in case of variational crimes

Petr Knobloch

Applications of Mathematics (2000)

  • Volume: 45, Issue: 2, page 99-129
  • ISSN: 0862-7940

Abstract

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We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.

How to cite

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Knobloch, Petr. "A finite element convergence analysis for 3D Stokes equations in case of variational crimes." Applications of Mathematics 45.2 (2000): 99-129. <http://eudml.org/doc/33051>.

@article{Knobloch2000,
abstract = {We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.},
author = {Knobloch, Petr},
journal = {Applications of Mathematics},
keywords = {Stokes equations; nonstandard boundary conditions; finite element method; approximation of boundary; Stokes equations; nonstandard boundary conditions; finite element method; approximation of boundary},
language = {eng},
number = {2},
pages = {99-129},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A finite element convergence analysis for 3D Stokes equations in case of variational crimes},
url = {http://eudml.org/doc/33051},
volume = {45},
year = {2000},
}

TY - JOUR
AU - Knobloch, Petr
TI - A finite element convergence analysis for 3D Stokes equations in case of variational crimes
JO - Applications of Mathematics
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 2
SP - 99
EP - 129
AB - We investigate a finite element discretization of the Stokes equations with nonstandard boundary conditions, defined in a bounded three-dimensional domain with a curved, piecewise smooth boundary. For tetrahedral triangulations of this domain we prove, under general assumptions on the discrete problem and without any additional regularity assumptions on the weak solution, that the discrete solutions converge to the weak solution. Examples of appropriate finite element spaces are given.
LA - eng
KW - Stokes equations; nonstandard boundary conditions; finite element method; approximation of boundary; Stokes equations; nonstandard boundary conditions; finite element method; approximation of boundary
UR - http://eudml.org/doc/33051
ER -

References

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  7. Variational crimes in a finite element discretization of 3D Stokes equations with nonstandard boundary conditions, East-West J. Numer. Math. 7 (1999), 133–158. (1999) Zbl0958.76043MR1699239
  8. Les Méthodes Directes en Théorie des Équations Elliptiques, Academia, Praha, 1967. (1967) MR0227584
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