Overcoming the problem of locking in linear elasticity and poroelasticity: An heuristic approach

Computational Geosciences

Volumn 13, Issue 1, 2009, Pages 5-12

  Phillips, Phillip Joseph ^a   Wheeler, Mary F ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b The University of Texas at Austin   (United States)

Author keywords

Discontinuous Galerkin; Linear elasticity; Locking; Poroelasticity

Indexed keywords

ELASTICITY; GALERKIN METHODS; HEURISTIC METHODS;

ELASTICITY; GALERKIN METHOD; HEURISTICS; LINEARITY; POROELASTICITY;

EID: 61549124733     PISSN: 14200597     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10596-008-9114-x     Document Type: Article

References (16)

1. Alberty, J., Carstensen, C., Funken, S., Klose, R.: Matlab implementation of the finite element method in elasticity. Computing 69, 239-263 (2002)
2. Barry, S., Mercer, G.: Exact solutions for two-dimensional time dependent flow and deformation within a poroelastic medium. J. Appl. Mech. 66, 536-540 (1999)
3. Biot, M.: General theory of three-dimensional consolidation. J. Appl. Phys. 2, 155-164 (1941)
4. Biot, M.: Theory of elasticity and consolidation for a porous anisotropic media. J. Appl. Phys. 26(2), 182-185 (1955)
5. Bowen, R.: Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18, 1129-1148 (1980)
6. Bowen, R.: Compressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 20, 697-735 (1982)
7. Brenner, S., Scott, L.: The Mathematical Theory of Finite Element Methods. Springer, New York (1994)
8. Lewis, R., Schrefler, B.: The Finite Element Method in Static and Dynamic Deformation and Consolidation of Porous Media. Wiley, Chichester (1987)
9. Liu, R.: Discontinuous Galerkin finite element solution for poromechanics. Ph.D. thesis, University of Texas at Austin (2004)
10. Mei, C., Auriault, J.-L.: Mechanics of heterogenous porous media with several spatial scales. Proc. R. Soc. Lond., A Math. Phys. Sci. 426(1871), 391-423 (1989)
11. Murad, M., Thomée, V., Loula, A.: Asymptotic behavior of semidiscrete finite element approximations of Biot's consolidation problem. SIAM J. Numer. Anal. 33, 1065-1083 (1996)
12. Phillips, P.J., Wheeler, M.F.: A coupling of mixed and continuous Galerkin finite element methods for poroelesticity I: The continuous in time case. Comput. Geosci. 11, 131-144 (2007)
13. Phillips, P.J., Wheeler, M.F.: A coupling of mixed and continuous Galerkin finite element methods for poroelesticity II: The discrete in time case. Comput. Geosci. (2008). doi: 10.1007/s10596-007-9044-z
14. Phillips, P.J., Wheeler, M.F.: A coupling of mixed and discontinuous Galerkin finite element methods for poroelesticity. Comput. Geosci. (2008). doi: 10.1007/s10596-008-9082-1
15. Rivière, B., Wheeler, M.: Optimal error estimates applied to linear elasticity. Technical report, ICES Report (2000)
16. Wan, J.: Stabalized finite element methods for coupled geomechanics and multiphase flow. Ph.D. thesis, Stanford University, Petroleum Eng. Dept. (2002)