Discontinuous finite element methods for incompressible flows on subdomains with non-matching interfaces

Computer Methods in Applied Mechanics and Engineering

Volumn 195, Issue 25-28, 2006, Pages 3274-3292

  Rivière, Béatrice ^a   Girault, Vivette ^b  

^a UNIVERSITY OF PITTSBURGH   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Backstep channel; Driven cavity; Hanging nodes; Navier Stokes; NIPG; SIPG; Stokes

Indexed keywords

ERROR ANALYSIS; ESTIMATION; GALERKIN METHODS; INCOMPRESSIBLE FLOW; INTERFACES (MATERIALS); NAVIER STOKES EQUATIONS;

BACKSTEP CHANNEL; DISCONTINOUS GALERKIN METHODS; DRIVEN CAVITY; HANGING NODES;

FINITE ELEMENT METHOD;

ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; GALERKIN METHODS; INCOMPRESSIBLE FLOW; INTERFACES (MATERIALS); NAVIER STOKES EQUATIONS;

EID: 33645903592     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2005.06.014     Document Type: Article

References (16)

1. Babuška I. The finite element method with Lagrangian multipliers. Numer. Math. 20 (1973) 179-192
2. Brezzi F. On the existence, uniqueness and approximation of the saddle-point problems arising from Lagrangian multipliers. R.A.I.R.O. 8 (1974) 129-151
3. Brezzi F., Marini L.D., and Süli E. Discontinuous Galerkin methods for first-order hyperbolic problems. Math. Mod. Meth. Appl. Sci. 14 (2004) 1893-1903
4. Ciarlet P. The Finite Element Methods for Elliptic Problems (1978), North-Holland, Amsterdam
5. Cockburn B., Kanschat G., and Schotzau D. The local discontinuous Galerkin method for the Oseen equations. Math. Comput. 73 (2004) 569-593
6. Crouzeix M., and Falk R.S. Non conforming finite elements for the Stokes problem. Math. Comput. 52 186 (1989) 437-456
7. Crouzeix M., and Raviart P.A. Conforming and non conforming finite element methods for solving the stationary Stokes equations. R.A.I.R.O. Numer. Anal. R3 (1973) 33-76
8. Fortin M., and Soulié M. A non-conforming piecewise quadratic finite element on triangles. Int. J. Numer. Methods Engrg. 19 (1983) 505-520
9. Girault V., and Raviart P.A. Finite element methods for Navier-Stokes equations: theory and algorithms. Springer Series in Computational Mathematics 5 (1986)
10. Girault V., Rivière B., and Wheeler M.F. A discontinuous Galerkin method with non-overlapping domain decomposition for the Stokes and Navier-Stokes problems. Math. Comput. 74 (2005) 53-84
11. V. Girault, B. Rivière, M.F. Wheeler, A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations, Technical Report TR-MATH 04-08, University of Pittsburgh, 2004.
12. S. Kaya, B. Rivière, A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations, SIAM J. Numer. Anal., in press.
13. Lesaint P., and Raviart P.A. On a finite element method for solving the neutron transport equation. In: de Boor C.A. (Ed). Mathematical Aspects of Finite Element Methods in Partial Differential Equations (1974), Academic Press, NY 89-123
14. Raviart P.A., and Thomas J.M. A mixed finite element method for second order elliptic problems. Mathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics 606 (1975), Springer-Verlag, Berlin
15. Schotzau D., Schwab C., and Toselli A. Mixed hp-DGFEM for incompressible flows. SIAM J. Numer. Anal. 40 6 (2002) 2171-2194
16. A. Toselli, L. Filippini, hp finite element approximations on non-matching grids for the Stokes problem, Technical Report 2002-22, ETHZ, 2002.