Mimetic finite differences for elliptic problems
Franco Brezzi; Annalisa Buffa; Konstantin Lipnikov
ESAIM: Mathematical Modelling and Numerical Analysis (2008)
- Volume: 43, Issue: 2, page 277-295
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- P.B. Bochev and J.M. Hyman, Principles of mimetic discretizations of differential operators, IMA Hot Topics Workshop on Compatible Spatial Discretizations142, D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides and M. Shashkov Eds., Springer-Verlag (2006).
- S. Brenner and L. Scott, The mathematical theory of finite element methods. Springer-Verlag, Berlin/Heidelberg (1994).
- F. Brezzi and A. Buffa, General framework for cochain approximations of differential forms. Technical report, Instituto di Mathematica Applicata a Technologie Informatiche (in preparation).
- F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes. SIAM J. Numer. Anal.43 (2005) 1872–1896.
- F. Brezzi, K. Lipnikov and V. Simoncini, A family of mimetic finite difference methods on polygonal and polyhedral meshes. Math. Mod. Meth. Appl. Sci.15 (2005) 1533–1552.
- F. Brezzi, K. Lipnikov and M. Shashkov, Convergence of mimetic finite difference method for diffusion problems on polyhedral meshes with curved faces. Math. Mod. Meth. Appl. Sci.16 (2006) 275–297.
- F. Brezzi, K. Lipnikov, M. Shashkov and V. Simoncini, A new discretization methodology for diffusion problems on generalized polyhedral meshes. Comput. Methods Appl. Mech. Engrg.196 (2007) 3692–3692.
- J. Campbell and M. Shashkov, A tensor artificial viscosity using a mimetic finite difference algorithm. J. Comput. Phys.172 (2001) 739–765.
- P.G. Ciarlet, The finite element method for elliptic problems. North-Holland, New York (1978).
- M. Dauge, Elliptic boundary value problems on corner domains: smoothness and asymptotics of solutions. Springer-Verlag, Berlin, New York (1988).
- P. Dvorak, New element lops time off CFD simulations. Mashine Design78 (2006) 154–155.
- S.L. Lyons, R.R. Parashkevov and X.H. Wu, A family of H1-conforming finite element spaces for calculations on 3D grids with pinch-outs. Numer. Linear Algebra Appl.13 (2006) 789–799.
- L. Margolin, M. Shashkov and P. Smolarkiewicz, A discrete operator calculus for finite difference approximations. Comput. Meth. Appl. Mech. Engrg.187 (2000) 365–383.
- P.A. Raviart and J.-M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method, I. Galligani and E. Magenes Eds., Springer-Verlag, Berlin-Heilderberg-New York (1977) 292–315.
Citations in EuDML Documents
top- F. Brezzi, Richard S. Falk, L. Donatella Marini, Basic principles of mixed Virtual Element Methods
- Robert Eymard, Cindy Guichard, Raphaèle Herbin, Small-stencil 3D schemes for diffusive flows in porous media
- Robert Eymard, Cindy Guichard, Raphaèle Herbin, Small-stencil 3D schemes for diffusive flows in porous media
- Jérôme Bonelle, Alexandre Ern, Analysis of Compatible Discrete Operator schemes for elliptic problems on polyhedral meshes
- Imbunm Kim, Zhongxuan Luo, Zhaoliang Meng, Hyun NAM, Chunjae Park, Dongwoo Sheen, A piecewise P2-nonconforming quadrilateral finite element