Multiscale discontinuous Galerkin methods for elliptic problems with multiple scales

Lecture Notes in Computational Science and Engineering

Volumn 44, Issue , 2005, Pages 1-20

  Aarnes, Jørg ^a   Heimsund, Bjørn Ove ^b  

^a SINTEF   (Norway)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

Discontinuous Galerkin methods; Elliptic partial differential equations; Multiscale methods

Indexed keywords

GLASS CERAMICS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS;

APPROXIMATION SPACES; CONTINUITY CONSTRAINTS; DISCONTINUOUS GALERKIN METHODS; ELLIPTIC PARTIAL DIFFERENTIAL EQUATION; ELLIPTIC PROBLEM; FLOWS IN POROUS MEDIA; MULTISCALE METHOD; NUMERICAL COMPARISON;

GALERKIN METHODS;

EID: 84880297064     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-26444-2_1     Document Type: Article

References (16)

1. J. Aarnes, On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation, Multiscale Model. Simul., 2, 421-439, (2004).
2. J. Aarnes, Efficient domain decomposition methods for elliptic problems in heterogeneous porous media, to appear in Comput. Vis. Science.
3. J. Aarnes, T. Y. Hou, Multiscale domain decomposition methods for elliptic problems with high aspect ratios, Acta Math. Appl. Sinica, 18, 63-76, (2002).
4. D. N. Arnold, An Interior Penalty Finite Element Method with Discontinuous Elements, SIAM J. Numer. Anal., 19, 742-760, (1982).
5. D. N. Arnold, F. Brezzi, B. Cockburn, L. D. Marini, Unified Analysis of Discontinuous Galerkin Methods, SIAM J. Numer. Anal., 39, 1749-1779 (2002).
6. F. Bassi, S. Rebay, A High-Order Accurate Discontinuous Finite Element Method for the Numerical Solution of the Compressible Navier Stokes Equations, J. Comput. Phys., 131, 267-279, (1997).
7. F. Brezzi, G. Manzini, D. Marini, P. Pietra, A. Russo, Discontinuous Finite Elements for Diffusion Problems, in Atti Convegno in onore di F. Brioschi (Milan 1997), Instituto Lombardo, Accademia di Scienze e Lettere, Milan, Italy, 197-217, (1999).
8. P. Castillo, B. Cockburn, I. Perugia, D. Schötzau, An a priori error analysis of the Local Discontinuous Galerkin Method for Elliptic Problems, SIAM J. Numer. Anal., 38, 1676-1706, (2000).
9. Z. Chen and T. Y. Hou, A mixed multiscale finite element method for elliptic problems with oscillating coefficients, Math. Comp., 72, 541-576, (2003).
10. B. Cockburn, G. Karniadakis, C.-W. Shu (eds). Discontinuous Galerkin Methods. Theory, Computation and Applications, Lect. Notes Comput. Sci. Eng., 11, Springer-Verlag, Heidelberg, (2000).
11. D. Douglas, Jr, T. Dupont, Interior Penalty Procedures for Elliptic and Parabolic Galerkin Methods, Lect. Notes Phys., 58, Springer-Verlag, Berlin, (1976).
12. T. Y. Hou, X.-H. Wu, A Multiscale Finite Element Method for Elliptic Problems in Composite Materials and Porous Media, J. Comput. Phys., 134, 169-189, (1997).
13. T. Y. Hou, X.-H. Wu, Z. Cai, Convergence of a Multiscale Finite Element Method for Elliptic Problems with Rapidly Oscillating Coefficients, Math. Comp, 68, 913-943, (1999).
14. J.-L. Lions, Problèmes aux limites non homogènes à donées irrégulières: Une method d'approximation, Num. Anal. Part. Diff. Eqn. (C.I.M.E. 2 Ciclo, Ispra, 1967), Edizioni Cremonese, Rome, 283-292, (1968).
15. P. A. Raviart and J. M. Thomas, A mixed finite element method for second order elliptic equations, Mathematical Aspects of Finite Element Methods (I. Galligani and E. Magenes, eds.), Springer-Verlag, Berlin - Heidelberg - New York, 292-315, (1977).
16. M. F. Wheeler, An Elliptic Collocation-Finite Element Method with Interior Penalties, SIAM J. Numer. Anal., 15, 152-161, (1978).