A discrete de Rham complex with enhanced smoothness

Calcolo

Volumn 43, Issue 4, 2006, Pages 287-306

  Tai, Xue Cheng ^a   Winther, Ragnar ^b  

^a UNIVERSITY OF BERGEN   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSIFICATION (OF INFORMATION); FLOW OF FLUIDS; STABILITY;

DISCRETIZATIONS; FINITE ELEMENT SPACE; FUNDAMENTAL TOOLS; SINGULAR PERTURBATION PROBLEMS; STABILITY PROPERTIES; STABLE ELEMENTS; STANDARD REQUIREMENTS; THREE SPACE DIMENSIONS; TYPE SYSTEMS; UNIFORM STABILITY;

FINITE ELEMENT METHOD;

EID: 33846372237     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-006-0124-6     Document Type: Article

References (15)

1. Arnold, D.N., Falt, R.S., Winther, R.: Differential complexes and stability of finite element methods. I. The de Rham complex. In: Arnold, D.N. et al. (eds.): Compatible spatial discretizations. (The IMA Volumes in Mathematics and its Applications 142) Berlin: Springer (2006), pp. 23-46
2. Arnold, D.N., Falk, R.S., Winther, R.: Finite element exterior calculus, homological techniques, and applications. Acta Numerica 15, 1-155 (2006)
3. 1 vector fields. Math. Comp. 73, 1067-1087 (2004)
4. Brezzi, F.: On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Rev. Française Automat. Informat. Recherche Opérationelle Sér. Rouge 8, 129-151 (1974)
5. Brezzi, F., Douglas, J., Marini, L.D.: Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47, 217-235 (1985)
6. Brezzi, F., Fortin, M.: Mixed and hybrid finite element methods. Berlin: Springer 1991
7. Brezzi, F., Fortin, M., Marini, L.D.: Mixed finite element methods with continuous stress. Math. Models Methods Appl. Sci. 3, 275-287 (1993)
8. Dauge, M.: Stationary Stokes and Navier-Stokes systems on two- and three-dimensional domains with corners. I. Linearized equations. SIAM J. Math. Anal. 20, 74-97 (1989)
9. Girault, V., Raviart, P.-A.: Finite element methods for Navier-Stokes equations. Berlin: Springer 1986
10. Mardal, K.-A., Tai, X-C, Winther, R.: A robust finite element method for Darcy-Stokes flow. SIAM J. Num. Anal. 40, 1605-1631 (2002)
11. Mardal, K.-A., Winther, R.: An observation on Korn's inequality for nonconforming finite element methods. Math. Comp. 75, 1-6 (2005)
12. 3. Numer. Math. 35, 315-341 (1980)
13. 3. Numer. Math. 50, 57-81 (1986)
14. 2-element. Math. Comp. 70, 489-505 (2001)
15. nd order elliptic problems. In: Galligani, I.; Magenes, E. (eds.): Mathematical aspects of finite element methods. (Lecture Notes in Mathematics 606) Berlin: Springer (1977), pp. 292-315