Finite differences and boundary element methods for non-stationary viscous incompressible flow

Werner Varnhorn

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 135-154
  • ISSN: 0137-6934

Abstract

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We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out.

How to cite

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Varnhorn, Werner. "Finite differences and boundary element methods for non-stationary viscous incompressible flow." Banach Center Publications 29.1 (1994): 135-154. <http://eudml.org/doc/262880>.

@article{Varnhorn1994,
abstract = {We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out.},
author = {Varnhorn, Werner},
journal = {Banach Center Publications},
keywords = {implicit fractional step procedure; time discretization; convergence; Sobolev spaces; collocation},
language = {eng},
number = {1},
pages = {135-154},
title = {Finite differences and boundary element methods for non-stationary viscous incompressible flow},
url = {http://eudml.org/doc/262880},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Varnhorn, Werner
TI - Finite differences and boundary element methods for non-stationary viscous incompressible flow
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 135
EP - 154
AB - We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out.
LA - eng
KW - implicit fractional step procedure; time discretization; convergence; Sobolev spaces; collocation
UR - http://eudml.org/doc/262880
ER -

References

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  13. [12] R. Leis, Vorlesungen über partielle Differentialgleichungen zweiter Ordnung, Bibliographisches Institut, Mannheim 1967. 
  14. [13] M. Mc Cracken, The resolvent problem for the Stokes equations on halfspace in L p , SIAM J. Math. Anal. 12 (1981), 201-228. 
  15. [14] F. K. G. Odquist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z. 32 (1930), 329-375. Zbl56.0713.04
  16. [15] W. I. Smirnow, Lehrgang der höheren Mathematik 4, Deutscher Verlag der Wissenschaften, Berlin 1979. 
  17. [16] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1977. 
  18. [17] W. Varnhorn, Efficient quadrature for a boundary element method to compute threedimensional Stokes flow, Internat. J. Numer. Methods Fluids 9 (1989), 185-191. Zbl0658.76034

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