Research in Numerical Fluid mechanics pp 18-29 | Cite as

# On the Computation of Free Boundaries

- 2 Citations
- 29 Downloads

## Abstract

Problems in which the solution of a (partial) differential equation has to satisfy certain conditions on the boundary of a prescribed domain are referred to as boundary-value problems. In many cases, however, the boundary of the domain is not known in advance but has to be determined as part of the solution. The term *stationary free-boundary* (SFB) is commonly used when the boundary is stationary and a steady-state exists. *Moving free boundaries* (MFB), on the other hand, are associated with time-dependent problems and the position of the boundary now is a function of time and space. In applications, SFB problems are usually of elliptic type, while MFB problems are often described by parabolic equations. We refer to [l] which presents a broad and detailed account of the mathematical (both analytical and numerical) solution of FB problems.

## Preview

Unable to display preview. Download preview PDF.

## References

- [1]J. Crank: Free and moving boundary problems. Oxford Science Publications, 1984.zbMATHGoogle Scholar
- [2]C. Cuvelier: Report 82–0 9, Delft University of Technology 1982.Google Scholar
- [3]C. Cuvelier: Comp. Meth. Appl. Mech. Engng, 48, 1985, p.45–80.MathSciNetADSzbMATHCrossRefGoogle Scholar
- [4]C. Cuvelier: to appear.Google Scholar
- [5]C. Cuvelier, J.M. Driessen: J. Fluid Mech. 16 9, 1986, p 1–26.ADSCrossRefGoogle Scholar
- [6]C. Cuvelier, A. Segal, A.A. van Steenhoven: Finite-element analysis and Navier-Stokes equations, Reidel Publ. Comp., 1986.CrossRefGoogle Scholar
- [7]A. Dervieux: Rapports de Recherche INRIA, 67, 68 (1981).Google Scholar
- [8]P.R. Garabedian: Bull. Amer. Math. Soc. 62, 1956, p. 219–235.MathSciNetzbMATHCrossRefGoogle Scholar
- [9]N. Kruyt: Master’s thesis, Delft University of Technology, 1985.Google Scholar
- [10]N. Kruyt, C. Cuvelier, A. Segal, J. v.d. Zanden: Submitted to Int. J. Num. Meth. Fluids.Google Scholar
- [11]R. Glowinski, J.L. Lions, R. Tramolieres: Numerical analysis of variational inequalities. North-Holland, 1981.zbMATHGoogle Scholar
- [12]C. Vuik C. Cuvelier: J. Comp. Physics 59, 1985, p. 247–263.ADSzbMATHCrossRefGoogle Scholar