Adaptive variational multiscale methods based on a posteriori error estimation: Duality techniques for elliptic problems

Lecture Notes in Computational Science and Engineering

Volumn 44, Issue , 2005, Pages 181-193

  Larson, Mats G ^a   Målqvist, Axel ^b  

^a UMEÅ UNIVERSITY   (Sweden)

^b CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

A posteriori error estimation; Duality techniques; Elliptic problems; Finite element method; Variational multiscale method

Indexed keywords

ERRORS; VARIATIONAL TECHNIQUES;

A-POSTERIORI ERROR ESTIMATIONS; DISCRETIZATION ERRORS; DUALITY TECHNIQUES; ELLIPTIC PROBLEM; MULTISCALE FINITE ELEMENT METHOD; PARALLEL SOLUTIONS; SECOND-ORDER PARTIAL DIFFERENTIAL EQUATION; VARIATIONAL MULTISCALE METHODS;

FINITE ELEMENT METHOD;

EID: 84880265375     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-26444-2_9     Document Type: Article

References (11)

1. T. Arbogast and S. L. Bryant, A two-scale numerical subgrid technique for waterflood simulations, SPE J., Dec. 2002, pp 446-457.
2. B. Aksoylu, S. Bond, and M. Holst An odyssey into local refinement and multilevel preconditioning III: Implementation of numerical experiments, SIAM J. Sci. Comput., 25(2003), 478-498.
3. B. Aksoylu and M. Holst An odyssey into local refinement and multilevel preconditioning I: Optimality of the BPX preconditioner, SIAM J. Numer. Anal. (2002) in review
4. B. Aksoylu and M. Holst An odyssey into local refinement and multilevel preconditioning II: stabilizing hierarchical basis methods, SIAM J. Numer. Anal. in review
5. S. C. Brenner and L. R. Scott, The mathematical theory of finite element methods, Springer Verlag, 1994.
6. T. Y. Hou and X.-H. Wu, A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys. 134 (1997) 169-189.
7. T. J. R. Hughes, Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, Comput. Methods Appl. Mech. Engrg. 127 (1995) 387-401.
8. T. J. R. Hughes, L Mazzei, A. A. Oberai, and M. G. Larson, The continuous Galerkin method is locally conservative, J. Comput. Phys., Vol. 163(2) (2000) 467-488.
9. T. J. R. Hughes, G. R. Feijóo, L. Mazzei and Jean-Baptiste Quincy, The variational multiscale method - a paradigm for computational mechanics, Comput. Methods Appl. Mech. Engrg. 166 (1998) 3-24.
10. M. G. Larson and A. Målqvist, Adaptive Variational Multiscale Methods Based on A Posteriori Error Estimates: Energy Norm Estimates for Elliptic Problems, preprint
11. A. A. Oberai and P. M. Pinsky, A multiscale finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg. 154 (1998) 281-297.