A stokes interface problem: Stability, finite element analysis and a robust solver

ECCOMAS 2004 - European Congress on Computational Methods in Applied Sciences and Engineering

Volumn , Issue , 2004, Pages

  Olshanskii, Maxim A ^a   Reuskent, Arnold ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Finite elements; Interface problem; Preconditioning; Stokes equations; Two phase flows

Indexed keywords

DISCRETIZATION ERRORS; INTERFACE PROBLEMS; NUMERICAL EXPERIMENTS; PRECONDITIONING; ROBUST PRECONDITIONER; STOKES EQUATIONS; VARIATIONAL FORMULATION; VISCOSITY COEFFICIENT;

COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; NAVIER STOKES EQUATIONS;

VISCOSITY;

EID: 84893507925     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. J.U. Brackbill, D.B. Kothe, and C. Zemach. A continuum method for modeling surface tension. J. Comput. Phys., 100, 335-354, 1992.
2. I. Babuska. The finite element method for elliptic problems with discontinuous coefficients. Computing, 5, 277-213, 1970.
3. I. Babuska, C. Caloz and J. Osborn. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal., 31, 945-981, 1994.
4. C. Bernardi, R. Verfürth. Adaptive finite element methods for elliptic equations with non-smooth coefficients. Numer. Math., 85, 579-608, 2000.
5. J.H. Bramble. Multigrid Methods. Pitman Research Notes in Mathematics, Vol. 294, John Wiley, New York, 1993.
6. J.H. Bramble and J.T. King. A finite element method for interface problems in domains with smooth boundaries and interfaces. Advances in Comp. Math., 6, 109-138, 1996.
7. J.H. Bramble, J.E. Pasciak, J. Wang and J. Xu. Convergence estimates for multigrid algorithms without regularity assumptions. Math. Comp., 57, 23-45, 1991.
8. Y.C. Chang, T.Y. Hou, B. Merriman, and S. Osher. Eulerian capturing methods based on a level set formulation for incompressible fluid interfaces. J. Comput. Phys., 124, 449-464, 1996.
9. Z. Chen and J. Zou. Finite element method and its convergence for elliptic and parabolic interface problems. Numer. Math., 79, 175-202, 1998.
10. P.G. Ciarlet. Basic Error Estimates for Elliptic Problems. in Handbook of Numerical Analysis, Vol. II, P.G. Ciarlet and J.L. Lions, eds., Elsevier Science, 1991.
11. V. Girault and P.-A. Raviart. Finite Element Methods for Navier-Stokes Equations. Springer, Berlin, 1986.
12. M.A. Olshanskii, A. Reusken. Analysis of a Stokes interface problem. IGPM report, 237, RWTH-Aachen, 2004. Submitted.
13. S. Osher and R.P. Fedkiw. Level set methods: An overview and some recent results. J. Comput. Phys., 169, 463-502, 2001.
14. M. Petzoldt. A posteriori error estimators for elliptic equations with discontinuous diffusion coefficients. Advances in Computational Mathematics, 16, 47-75, 2002.
15. C. Powell and D. Silvester. Black-box preconditioning for mixed formulation of self-adjoint elliptic PDEs. In: Challenges in Scientific Computing - CISC 2002, ed. E. Bänsch. Lecture Notes in Computational Science and Engineering, 35, 268-285, 2003.
16. A.-K. Tornberg and B. Engquist. A finite element based level-set method for multiphase flow applications. Comput. Visual. Sci., 3, 93-101, 2000.
17. M. Plum and C. Wieners. Optimal a priori estimates for interface problems. Numer. Math., 95, 735-759, 2003.
18. D. Silvester, A. Wathen. Fast iterative solution of stabilised stokes systems. part II: using general block preconditioners. SIAM J. Numer. Anal., 31, 1352-1367, 1994.
19. A. Wathen. Realistic eigenvalues bounds for the Galerkin mass matrix. IMA J. Nu-mer. Anal., 7, 449-457, 1987.
20. H. Yserentant. Two preconditioners based on the multi-level splitting of finite element spaces. Numer. Math., 58, 163-184, 1990.