Error analysis of variable degree mixed methods for elliptic problems via hybridization

Mathematics of Computation

Volumn 74, Issue 252, 2005, Pages 1653-1677

  Cockburn, Bernardo ^a   Gopalakrishnan, Jayadeep ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF FLORIDA   (United States)

Author keywords

Elliptic problems; Hybrid methods; Mixed finite elements

Indexed keywords

EID: 27144538207     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-05-01741-2     Document Type: Article

References (16)

1. T. ARBOGAST AND Z. CHEN, On the implementation of mixed methods as nonconforming methods for second-order elliptic problems, Math. Comp., 64 (1995), pp. 943-972. MR1303084 (95k:65102)
2. D. N. ARNOLD AND F. BREZZI, Mixed and non-conforming finite element methods: implementation, post-processing and error estimates, Model. Math. Anal.Numér., 19 (1985), pp. 7-35. MR0813687 (87g:65126)
3. P. BRENNER AND L. R. SCOTT, The mathematical theory of finite element methods, vol. 15 of Texts in Applied Mathematics, Springer Verlag, 1994. MR1278258 (95f:65001)
4. F. BREZZI, J. DOUGLAS, JR., AND D. MARINI, Two families of mixed finite elements for second order elliptic problems, Numer. Math., 47 (1985), pp. 217-235. MR0799685 (87g:65133)
5. _, Variable degree mixed methods for second order elliptic problems, Mat. Aplic. e Comp., 4 (1985), pp. 19-34. MR0808322 (87d:65129)
6. F. BREZZI AND M. FORTIN, Mixed and Hybrid finite element methods, Springer Verlag, 1991. MR1115205 (92d:65187)
7. B. COCKBURN AND J. GOPALAKRISHNAN, A characterization of hybridized mixed methods for the Dirichlet problem, SIAM J. Numer. Anal., 42 (2004), pp. 283-301. MR2051067
8. L. DEMKOWICZ, P. MONK, L. VARDAPETYAN, AND W. RACHOWICZ, De Rham diagram for hp finite element spaces, Comput. Math. Appl., 39 (2000), pp. 29-38. MR1746160 (2000m:78052)
9. B. M. FRAEJIS DE VEUBEKE, Displacement and equilibrium models in the finite element method, in Stress Analysis, O. Zienkiewicz and G. Holister, eds., Wiley, New York, 1977, pp. 145-197.
10. G. N. GATICA, Solvability and Galerkin approximations of a class of nonlinear operator equations, Z. Anal. Anwendungen, 21 (2002), pp. 761-781. MR1929431 (2003h:65074)
11. G. N. GATICA, N. HEUER, AND S. MEDDAHI, On the numerical analysis of nonlinear twofold saddle point problems, IMA J. Numer. Anal., 23 (2003), pp. 301-330. MR1975268 (2004b:65183)
12. J. GOPALAKRISHNAN, A Schwarz preconditioner for a hybridized mixed method, Computational Methods in Applied Mathematics, 3 (2003), pp. 116-134. MR2002260 (2004g:65033)
13. R. KIRBY AND C. DAWSON, Private Communication (2003).
14. I. PERUGIA AND D. SCHÖTZAU, An hp-analysis of the local discontinuous Galerkin method for diffusion problems, J. Sci. Comput. (Special Issue: Proceedings of the Fifth International Conference on Spectral and High Order Methods (ICOSAHOM-01), Uppsala, Sweden), 17 (2002), pp. 561-571. MR1910752
15. P. RAVIART AND J. THOMAS, A mixed method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method, I. Galligani and E. Magenes, eds., Lecture Notes in Math. 606, Springer-Verlag, New York, 1977. MR0483555 (58:3547)
16. M. SURI, On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems, Math. Comp., 54 (1990), pp. 1-19. MR0990603 (90e:65164)