Abstract
The aim of this work is to analyze “Discrete Duality Finite Volume” schemes (DDFV for short) on general meshes by adapting the theory known for the linear Stokes problem with Dirichlet boundary conditions to the case of Neumann boundary conditions on a fraction of the boundary. We prove well-posedness for stabilized schemes and we derive some error estimates. Finally, we illustrate some numerical results in which we compare stabilized and unstabilized schemes.
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References
Boyer, F., Krell, S., Nabet, F.: Inf-Sup stability of the discrete duality finite volume method for the 2D Stokes problem. Math. Comput. 84, 2705–2742 (2015)
Chainais-Hillairet, C., Krell, S., Mouton, A.: Convergence analysis of a DDFV scheme for a system describing miscible fluid flows in porous media. Num. Methods PDEs 31(3), 723–760 (2015)
Delcourte, S.: Développement de méthodes de volumes finis pour la mécanique des fluides, Ph.D. thesis. http://tel.archives-ouvertes.fr/tel-00200833/fr/, Université Paul Sabatier, Toulouse, France (2007)
Domelevo, K., Omnes, P.: A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids. M2AN 39(6), 1203–1249 (2005)
Eymard, R., Gallouët, T., Herbin, R.: Finite Volume Methods. Handbook of Numerical Analysis, vol. VII. North-Holland, Amsterdam (2000)
Hermeline, F.: A finite volume method for the approximation of diffusion operators on distorted meshes. J. Comput. Phys. 160(2), 481–499 (2000)
Krell, S.: Stabilized DDFV schemes for Stokes problem with variable viscosity on general 2D meshes. Num. Methods PDEs 27(6), 1666–1706 (2011)
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Goudon, T., Krell, S., Lissoni, G. (2017). Numerical Analysis of the DDFV Method for the Stokes Problem with Mixed Neumann/Dirichlet Boundary Conditions. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects . FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 199. Springer, Cham. https://doi.org/10.1007/978-3-319-57397-7_29
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DOI: https://doi.org/10.1007/978-3-319-57397-7_29
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