Free Access
Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
---|---|---|
Page(s) | S103 - S147 | |
DOI | https://doi.org/10.1051/m2an/2020029 | |
Published online | 26 February 2021 |
- Y. Achdou and J.-L. Guermond, Convergence analysis of a finite element projection/Lagrange–Galerkin method for the incompressible Navier-Stokes equations. SIAM J. Numer. Anal. 37 (2000) 799–826. [Google Scholar]
- R. Adams and J. Fournier, Sobolev Spaces, Pure and Applied Mathematics. Elsevier Science (2003). [Google Scholar]
- G. Akrivis and B. Li, Maximum norm analysis of implicit–explicit backward difference formulas for nonlinear parabolic equations. IMA J. Numer. Anal. 38 (2018) 75–101. [CrossRef] [Google Scholar]
- G. Akrivis, B. Li and C. Lubich, Combining maximal regularity and energy estimates for time discretizations of quasilinear parabolic equations. Math. Comput. 86 (2017) 1527–1552. [Google Scholar]
- A.S. Almgren, J.B. Bell, P. Colella, L.H. Howell and M.L. Welcome, A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142 (1998) 1–46. [Google Scholar]
- A. Ashyralyev, S. Piskarev and L. Weis, On well-posedness of difference schemes for abstract parabolic equations in Lp([0, T]; E) spaces. Numer. Funct. Anal. Optim. 23 (2002) 669–693. [Google Scholar]
- J.B. Bell and D.L. Marcus, A second-order projection method for variable-density flows. J. Comput. Phys. 101 (1992) 334–348. [Google Scholar]
- D. Boffi and Stability of higher order triangular Hood-Taylor methods for the stationary stokes equations. Math. Models Methods Appl. Sci. 04 (1994) 223–235. [Google Scholar]
- S.C. Brenner and R. Scott, The Mathematical Theory of Finite Element Methods, 3rd ed. In: Texts in Applied Mathematics. Springer-Verlag, New York (2008). [Google Scholar]
- S. Brenner, J. Cui, Z. Nan and L. Sung, Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell’s equations. Math. Comput. 81 (2012) 643–659. [Google Scholar]
- C. Calgaro, E. Creusé and T. Goudon, An hybrid finite volume-finite element method for variable density incompressible flows. J. Comput. Phys. 227 (2008) 4671–4696. [Google Scholar]
- A.J. Chorin, Numerical solution of the Navier-Stokes equations. Math. Comput. 22 (1968) 745–762. [Google Scholar]
- M. Crouzeix and V. Thomée, The stability in Lp and Wp1 of the L2-projection onto finite element function spaces. Math. Comput. 48 (1987) 521–532. [Google Scholar]
- R. Danchin, Density-dependent incompressible fluids in bounded domains. J. Math. Fluid Mech. 8 (2006) 333–381. [CrossRef] [Google Scholar]
- D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods. In: Vol. 69 of Mathématiques et Applications. Springer, Berlin Heidelberg (2012). [CrossRef] [Google Scholar]
- G.P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. In: Springer Monographs in Mathematics. Springer-Verlag, New York, (2011). [CrossRef] [Google Scholar]
- H. Gao, B. Li and W. Sun, Stability and convergence of fully discrete Galerkin FEMs for the nonlinear thermistor equations in a nonconvex polygon. Numer. Math. 136 (2017) 383–409. [Google Scholar]
- M. Geissert, Discrete maximal Lp regularity for finite element operators. SIAM J. Numer. Anal. 44 (2006) 677–698. [Google Scholar]
- J. Geng and Z. Shen, The Neumann problem and Helmholtz decomposition in convex domains. J. Funct. Anal. 259 (2010) 2147–2164. [Google Scholar]
- V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. In: Springer Series in Computational Mathematics, Springer, Berlin Heidelberg (1986). [CrossRef] [Google Scholar]
- V. Girault, R. Nochetto and R. Scott, Maximum-norm stability of the finite element Stokes projection. J. Math. Pures Appl. 84 (2005) 279–330. [Google Scholar]
- P. Grisvard, Elliptic Problems in Nonsmooth Domains. Society for Industrial and Applied Mathematics (2011). [Google Scholar]
- J.L. Guermond and L. Quartapelle, A projection FEM for variable density incompressible flows. J. Comput. Phys. 165 (2000) 167–188. [Google Scholar]
- J.L. Guermond and A. Salgado, A fractional step method based on a pressure Poisson equation for incompressible flows with variable density. C. R. Math. 346 (2008) 913–918. [Google Scholar]
- J.L. Guermond and A. Salgado, A splitting method for incompressible flows with variable density based on a pressure Poisson equation. J. Comput. Phys. 228 (2009) 2834–2846. [Google Scholar]
- J.L. Guermond and A. Salgado, Error analysis of a fractional time-stepping technique for incompressible flows with variable density. SIAM J. Numer. Anal. 49 (2011) 917–940. [Google Scholar]
- J. Guermond, P. Minev and J. Shen, An overview of projection methods for incompressible flows. Comput. Methods Appl. Mech. Eng. 195 (2006) 6011–6045. [Google Scholar]
- J.G. Heywood and R. Rannacher, Finite-element approximation of the nonstationary Navier-Stokes problem part IV: error analysis for second-order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [Google Scholar]
- R.B. Kellogg and J.E. Osborn, A regularity for the Stokes problem in a convex polygon. J. Funct. Anal. 21 (1976) 397–431. [Google Scholar]
- B. Kovács, B. Li and C. Lubich, A-stable time discretizations preserve maximal parabolic regularity. SIAM J. Numer. Anal. 54 (2016) 3600–3624. [Google Scholar]
- P.C. Kunstmann, B. Li and C. Lubich, Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity. Found. Comput. Math. 18 (2018) 1109–1130. [CrossRef] [Google Scholar]
- O. Ladyzhenskaya and V. Solonnikov, Unique solvability of an initial- and boundary-value problem for viscous incompressible inhomogeneous fluids. J. Sov. Math. 9 (1978) 697–749. [CrossRef] [Google Scholar]
- B. Li, Maximum-norm stability and maximal Lp regularity of FEMs for parabolic equations with Lipschitz continuous coefficients. Numer. Math. 131 (2015) 489–516. [Google Scholar]
- B. Li, Analyticity, maximal regularity and maximum-norm stability of semi-discrete finite element solutions of parabolic equations in nonconvex polyhedra. Math. Comput. 88 (2019) 1–44. [Google Scholar]
- B. Li and W. Sun, Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media. SIAM J. Numer. Anal. 51 (2013) 1959–1977. [Google Scholar]
- B. Li and W. Sun, Linearized FE approximations to a nonlinear gradient flow. SIAM J. Numer. Anal. 52 (2014) 2623–2646. [Google Scholar]
- B. Li and W. Sun, Regularity of the diffusion-dispersion tensor and error analysis of FEMs for a porous media flow. SIAM J. Numer. Anal. 53 (2015) 1418–1437. [Google Scholar]
- B. Li and W. Sun, Maximal + analysis of finite element solutions for parabolic equations with nonsmooth coefficients in convex polyhedra. Math. Comput. 86 (2017) 1071–1102. [Google Scholar]
- B. Li and Z. Zhang, Mathematical and numerical analysis of time-dependent Ginzburg-Landau equations in nonconvex polygons based on Hodge decomposition. Math. Comput. 86 (2017) 1579–1608. [Google Scholar]
- Y. Li, L. Mei, J. Ge and F. Shi, A new fractional time-stepping method for variable density incompressible flows. J. Comput. Phys. 242 (2013) 124–137. [Google Scholar]
- Y. Li, J. Li, L. Mei and Y. Li, Mixed stabilized finite element methods based on backward difference/Adams–Bashforth scheme for the time-dependent variable density incompressible flows. Comput. Math. App. 70 (2015) 2575–2588. [Google Scholar]
- C. Liu and N.J. Walkington, Convergence of numerical approximations of the incompressible Navier-Stokes equations with variable density and viscosity. SIAM J. Numer. Anal. 45 (2007) 1287–1304. [Google Scholar]
- A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems. In: Vol. 16 of Progress in Nonlinear Differential Equations and their Applications. Birkhäuser Verlag (1995). [Google Scholar]
- E. Ortega-Torres, P. Braz e Silva and M. Rojas-Medar, Analysis of an iterative method for variable density incompressible fluids. Ann. Univ. Ferrara 55 (2009) 129. [CrossRef] [Google Scholar]
- A. Prohl, Projection and Quasi-Compressibility Methods for Solving the Incompressible Navier-Stokes Equations. In: Advances in Numerical Mathematics. Vieweg+Teubner Verlag (1997). [CrossRef] [Google Scholar]
- J.-H. Pyo and J. Shen, Gauge-Uzawa methods for incompressible flows with variable density. J. Comput. Phys. 221 (2007) 181–197. [Google Scholar]
- R. Rannacher, On Chorin’s Projection Method for the Incompressible Navier-Stokes Equations. Springer Berlin Heidelberg, Berlin, Heidelberg (1992) 167–183. [Google Scholar]
- J. Shen, On error estimates of projection methods for Navier-Stokes equations: first-order schemes. SIAM J. Numer. Anal. 29 (1992) 57–77. [Google Scholar]
- J. Shen, On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes. Math. Comput. 65 (1996) 1039–1065. [Google Scholar]
- E.M. Stein, Singular Integrals and Differentiability Properties of Functions. In: Monographs in Harmonic Analysis. Princeton University Press (1970). [Google Scholar]
- L. Tartar, An Introduction to Sobolev Spaces and Interpolation Spaces. In: Vol. 3 of Lecture Notes of the Unione Matematica Italiana. Springer-Verlag, Berlin Heidelberg (2007). [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.