%0 Journal Article %1 droniou2008study %A Droniou, Jérôme %A Eymard, Robert %D 2009 %J Numerical Methods for Partial Differential Equations %K 65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 76d05-incompressible-navier-stokes-equations 76d07-stokes-and-related-oseen-etc-flows 76m12-finite-volume-methods-in-fluid-mechanics %N 1 %P 137-171 %R 10.1002/num.20333 %T Study of the mixed finite volume method for Stokes and Navier‐Stokes equations %U https://onlinelibrary.wiley.com/doi/10.1002/num.20333 %V 25 %X We present finite volume schemes for Stokes and Navier‐Stokes equations. These schemes are based on the mixed finite volume introduced in (Droniou and Eymard, Numer Math 105 (2006), 35‐71), and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier‐Stokes equations, the convergence of the scheme toward a solution of the continuous problem.

@article{droniou2008study, abstract = {We present finite volume schemes for Stokes and Navier‐Stokes equations. These schemes are based on the mixed finite volume introduced in (Droniou and Eymard, Numer Math 105 (2006), 35‐71), and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier‐Stokes equations, the convergence of the scheme toward a solution of the continuous problem.}, added-at = {2020-11-05T06:48:52.000+0100}, author = {Droniou, Jérôme and Eymard, Robert}, biburl = {https://www.bibsonomy.org/bibtex/2fdfdcb60ad69cfc86307427b4cdb62b6/gdmcbain}, doi = {10.1002/num.20333}, interhash = {c8c6657709122259766d940dd15c469f}, intrahash = {fdfdcb60ad69cfc86307427b4cdb62b6}, journal = {Numerical Methods for Partial Differential Equations}, keywords = {65m12-pdes-ivps-stability-and-convergence-of-numerical-methods 76d05-incompressible-navier-stokes-equations 76d07-stokes-and-related-oseen-etc-flows 76m12-finite-volume-methods-in-fluid-mechanics}, month = jan, number = 1, pages = {137-171}, timestamp = {2021-01-22T00:37:03.000+0100}, title = {Study of the mixed finite volume method for Stokes and Navier‐Stokes equations}, url = {https://onlinelibrary.wiley.com/doi/10.1002/num.20333}, volume = 25, year = 2009 }