Convergence of mimetic finite difference discretizations of the diffusion equation

Journal of Numerical Mathematics

Volumn 9, Issue 4, 2001, Pages 265-284

  Berndtf, M ^a   Lipnikov, K ^a   Moultonf, D ^a   Shashkov, M ^a  

^a University of Houston   (United States)

Author keywords

error estimates; mimetic discretizations; mixed finite elements

Indexed keywords

BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD;

FINITE DIFFERENCE DISCRETIZATIONS;

PROBLEM SOLVING;

EID: 0035708126     PISSN: 15702820     EISSN: None     Source Type: Journal    
DOI: 10.1515/JNMA.2001.265     Document Type: Article

References (15)

1. D. Braess, Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge University Press, Cambridge, U.K., New York, 1997.
2. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. Springer Verlag, Berlin, 1991.
3. J. Campbell and M. Shashkov, A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comp. Phys. (2001) 172, 739-765.
4. P. G. Ciarlet, Basic Error Estimates for Elliptic Problems. In: Handbook of Numerical Analysis, Vol. II: Finite Element Methods (Eds. P. G. Ciarlet and J.-L. Lions). Elsevier/North Holland, Amsterdam, 1991, pp.17-352.
5. J. Hyman and M. Shashkov, Mimetic discretizations for Maxwell's equations and the equations of magnetic diffusion. Progress in Electromagnetic Research (2001) 32, 89-121.
6. J.Hyman, M.Shashkov, and S.Steinberg, The numerical solution of diffusion problems in strongly heterogeneous non-isotropic materials. J. Comp. Phys. (1997) 132, 130-148.
7. J. Hyman, M. Shashkov, and S. Steinberg, Inner products for discrete vector fields and accuracy of mimetic difference methods. Los Alamos National Laboratory. Report LA-UR-99-6181, January, 2000.
8. J. E. Morel, R. M. Roberts, and M. J. Shashkov, A local support-operators diffusion discretization scheme. J. Comp. Phys. (1998) 144, 17-51.
9. R. R. P. van Nooyen, An improved accuracy version of the mixed finite-element method for a second-order elliptic equation. J. Comp. Appl. Math. (1993) 47, 11-33.
10. P. A. Raviart and J. M. Thomas, A mixed finite element method for second order elliptic problems. In: Mathematical Aspects ofthe Finite Element Method (Eds. I. Galligani and E. Magenes). Springer-Verlag, Berlin-Heilderberg-New York, 1977, pp.292-315.
11. J. E. Roberts and J. M. Thomas, Mixed and Hybrid Methods. In: Handbook ofNumerical Analysis, Vol. II: Finite Element Methods (Eds. P. G. Ciarlet and J.-L. Lions). Elsevier/North Holland, Amsterdam, 1991, pp.523 - 640.
12. M.Shashkov and S.Steinberg, Solving diffusion equations with rough coefficients in rough grids. J. Comp. Phys. (1996) 129, 383-405.
13. J. Shen, Mixed finite element methods on distorted rectangular grids. Institute for Scientific Computation, Texas A&M University. Report ISC-94-13-MATH, July, 1994.
14. J. M. Thomas, Sur l'analyse numerique des methods d'elements finis hybrides et mixtes. Ph.D. Thesis, Universite Pierre et Marie Curie, Paris, 1977.
15. J.Wang and T.Mathew, Mixed finite element methods over quadritaterals. In: Third International Conference on Advances in Numerical Methods adn Applications (Eds. I. T. Dimov, B. Sedov, and P.Vassilevski). World Scientific, 1994, pp.203-214.