Free Access
Issue |
ESAIM: M2AN
Volume 49, Number 4, July-August 2015
|
|
---|---|---|
Page(s) | 1019 - 1046 | |
DOI | https://doi.org/10.1051/m2an/2014065 | |
Published online | 25 June 2015 |
- M.J. Ahn, H.Y. Lee and M.R. Ohm, Error estimates for fully discrete approximation to a free boundary problem in polymer technology. Appl. Math. Comput. 138 (2003) 227–238. [CrossRef] [Google Scholar]
- J. Thomas Beale, The initial value problem for the Navier–Stokes equations with a free surface. Commun. Pure Appl. Math. 34 (1981) 359–392. [CrossRef] [Google Scholar]
- B. Cockburn and C.-W. Shu, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. II. General framework. Math. Comput. 52 (1989) 411–435. [Google Scholar]
- B. Cockburn and C.-W. Shu, Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. J. Sci. Comput. 16 (2001) 173–261. [CrossRef] [MathSciNet] [Google Scholar]
- B. Cockburn, S. Hou and C.-W. Shu, The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case. Math. Comput. 54 (1990) 545–581. [Google Scholar]
- R. Danchin, Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients. Rev. Mat. Iberoamericana 21 (2005) 863–888. [CrossRef] [MathSciNet] [Google Scholar]
- V. Girault, B. Riviere and M.F. Wheeler, A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations. ESAIM: M2AN 39 (2005) 1115–1147. [CrossRef] [EDP Sciences] [Google Scholar]
- V. Girault, B. Riviere and M.F. Wheeler, A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems. Math. Comput. 74 (2005) 249 53–84. [CrossRef] [Google Scholar]
- J. Grooss and J.S. Hesthaven, A level set discontinuous Galerkin method for free surface flows. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3406–3429. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Guo and I. Tice, Local well-posedness of the viscous surface wave problem without surface tension. Anal. PDE 6 (2013) 287–369. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Guo and I. Tice, Almost exponential decay of periodic viscous surface waves without surface tension. Arch. Ration. Mech. Anal. 207 (2013) 459–531. [CrossRef] [Google Scholar]
- E. Hairer, C. Lubich and M. Roche, The numerical solution of differential-algebraic systems by Runge-Kutta methods. In vol. 1409 of Lect. Notes Math. Springer-Verlag, Berlin (1989). [Google Scholar]
- F.H. Harlow and J. Eddie Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (1965) 2182–2189. [Google Scholar]
- C.W. Hirt and B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1981) 201–225. [CrossRef] [Google Scholar]
- H.Y. Lee, Error analysis of finite element approximation of a Stefan problem with nonlinear free boundary condition. J. Appl. Math. Comput. 22 (2006) 223–235. [CrossRef] [MathSciNet] [Google Scholar]
- R.H. Nochetto and C. Verdi, An efficient linear scheme to approximate parabolic free boundary problems: error estimates and implementation. Math. Comput. 51 (1988) 27–53. [Google Scholar]
- M. Sussman and M.Y. Hussaini, A discontinuous spectral element method for the level set equation. J. Sci. Comput. 19 (2003) 479–500. [CrossRef] [Google Scholar]
- L.-H. Wang, On Korn’s inequality. J. Comput. Math. 21 (2003) 321–324. [Google Scholar]
- M.F. Wheeler, An elliptic collocation-finite element method with interior penalties. SIAM J. Numer. Anal. 15 (1978) 152–161. [CrossRef] [MathSciNet] [Google Scholar]
- L. Wu, Well-posedness and decay of the viscous surface wave. SIAM J. Math. Anal. 46 (2014) 2084–2135. [CrossRef] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.