An optimal C0 finite element algorithm for the 2D biharmonic problem: Theoretical analysis and numerical results

Numerische Mathematik

Volumn 90, Issue 1, 2001, Pages 19-46

  Amara, M ^a   Dabaghi, F ^b  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035540059     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100284     Document Type: Article

References (13)

1. 0 d'approximation du bilaplacien. Compt. Rendus de l'Academie Sci. Tome 319, 1327-1330, Serie I (1994)
2. 0 finite element for plane crack problem. INRIA Internal Research Report N 3379, 1998, March
3. Bernardi C., Girault V., Maday Y.: Mixed spectral element approximation of the Navier Stokes equations in the stream function and vorticity formulation. IMA J. Numerical Anal. 12, 565-608 (1992)
4. Brezzi F., Fortin M.: Mixed and hybrid finite element method. Springer Series in Computational Mathematics, 15. New York: Springer, 1991
5. Brezzi F., Fortin M., Marini L.D.: Mixed finite element methods with continuous stresses. Math. Models Methods Appl. Sci. 3, (2) 275-287 (1993)
6. Ciarlet P.G., Glowinski R.: Dual iterative techniques for solving a finite element approximation of the biharmonic equation. Berlin: Springer, 1984
7. Ciarlet P.G., Raviart P.A.: A mixed method for the biharmonic problem. Mathematical aspect of finite elements in partial differential equations pp. 125-145, Carl de Boor (ed.) New York: Academic Press, 1974
8. Girault V., Giroire J., Sequeira A.: A stream function-vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces. Math. Meth. Appl. Sci. 15, (5) 345-363 (1992)
9. Girault V., Raviart P.A.: Finite element methods for Navier-Stokes equations, Theory and Algorithms. Berlin: Springer, 1986
10. Glowinski R., Pironneau O.: Numerical methods for the first biharmonic equation and for the two dimensional Stokes problem. SIAM Rev. 17, 167-212 (1979)
11. Nitsche J.: Über ein variationsprinzip zur lösung von Dirichlet-problem bei verwendung von Teilräumen, die keinen randbedingungen unterworfen sind. Abh. Math. Sem. Univ. Hamburg 36, 9-15 (1970/1971)
12. Ruas V.: On formulations of vorticity systems for a viscous incompressible flow with numerical applications. ZAMM Z.angew Math. Mech. 74, (1) 43-55 (1994)
13. Scholz R.: A mixed method for fourth order problem using finite elements. RAIRO, Analyse Numerique 12, 85-90 (1978)