An analogue of grad-div stabilization in nonconforming methods for incompressible flows
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Mine Akbas | Leo G. Rebholz | Alexander Linke | Philipp W. Schroeder | A. Linke | M. Akbas | L. Rebholz
[1] D. Braess. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .
[2] Leo G. Rebholz,et al. A Connection Between Scott-Vogelius and Grad-Div Stabilized Taylor-Hood FE Approximations of the Navier-Stokes Equations , 2011, SIAM J. Numer. Anal..
[3] Raytcho D. Lazarov,et al. Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems , 2009, SIAM J. Numer. Anal..
[4] Alexander Linke,et al. Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier--Stokes equations , 2016 .
[5] A. Ern,et al. Mathematical Aspects of Discontinuous Galerkin Methods , 2011 .
[6] Dominique Pelletier,et al. Are fem solutions of incompressible flows really incompressible? (or how simple flows can cause headaches!) , 1989 .
[7] Philipp W. Schroeder,et al. Stabilised dG-FEM for incompressible natural convection flows with boundary and moving interior layers on non-adapted meshes , 2016, J. Comput. Phys..
[8] P. Hansbo,et al. Stabilized Crouzeix‐Raviart element for the Darcy‐Stokes problem , 2005 .
[9] Volker John,et al. On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows , 2015, SIAM Rev..
[10] Vivette Girault,et al. Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms , 1986, Springer Series in Computational Mathematics.
[11] M. Fortin,et al. Mixed Finite Element Methods and Applications , 2013 .
[12] Alexander Linke,et al. On velocity errors due to irrotational forces in the Navier-Stokes momentum balance , 2016, J. Comput. Phys..
[13] Alexander Linke. A divergence-free velocity reconstruction for incompressible flows , 2012 .
[14] T. Hughes,et al. Two classes of mixed finite element methods , 1988 .
[15] O. Dorok,et al. Aspects of Finite Element Discretizations for Solving the Boussinesq Approximation of the Navier-Stokes Equations , 1994 .
[16] Sander Rhebergen,et al. Analysis of a Hybridized/Interface Stabilized Finite Element Method for the Stokes Equations , 2016, SIAM J. Numer. Anal..
[17] Maxim A. Olshanskii,et al. Grad–div stabilization and subgrid pressure models for the incompressible Navier–Stokes equations , 2009 .
[18] L. Tobiska,et al. On spurious velocities in incompressible flow problems with interfaces , 2007 .
[19] Marek Stastna,et al. A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow , 2015, ArXiv.
[20] Colin J. Cotter,et al. A finite element exterior calculus framework for the rotating shallow-water equations , 2012, J. Comput. Phys..
[21] Martin Kronbichler,et al. A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow , 2016, J. Comput. Phys..
[22] Christoph Lehrenfeld,et al. Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations , 2017, SeMA Journal.
[23] Guido Kanschat,et al. A Note on Discontinuous Galerkin Divergence-free Solutions of the Navier–Stokes Equations , 2007, J. Sci. Comput..
[24] Thirupathi Gudi,et al. A new error analysis for discontinuous finite element methods for linear elliptic problems , 2010, Math. Comput..
[25] Leo G. Rebholz,et al. On the convergence rate of grad-div stabilized Taylor–Hood to Scott–Vogelius solutions for incompressible flow problems , 2011 .
[26] Guido Kanschat,et al. A locally conservative LDG method for the incompressible Navier-Stokes equations , 2004, Math. Comput..
[27] C. Holm,et al. Reducing spurious flow in simulations of electrokinetic phenomena. , 2016, The Journal of chemical physics.
[28] C. Bernardi,et al. Analysis of some finite elements for the Stokes problem , 1985 .
[29] Gert Lube,et al. Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics , 2017, Journal of Scientific Computing.
[30] M. Olshanskii,et al. Stable finite‐element calculation of incompressible flows using the rotation form of convection , 2002 .
[31] J. Schöberl. C++11 Implementation of Finite Elements in NGSolve , 2014 .
[32] Volker John,et al. On the parameter choice in grad-div stabilization for the Stokes equations , 2014, Adv. Comput. Math..
[33] Leo G. Rebholz,et al. Stabilizing poor mass conservation in incompressible flow problems with large irrotational forcing and application to thermal convection , 2012 .
[34] Christoph Lehrenfeld,et al. High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows , 2015, ArXiv.
[35] P. Raviart,et al. Conforming and nonconforming finite element methods for solving the stationary Stokes equations I , 1973 .
[36] Colin J. Cotter,et al. A Framework for Mimetic Discretization of the Rotating Shallow-Water Equations on Arbitrary Polygonal Grids , 2012, SIAM J. Sci. Comput..
[37] Daniel Arndt,et al. Local projection FEM stabilization for the time‐dependent incompressible Navier–Stokes problem , 2015 .
[38] Rüdiger Verfürth,et al. Error estimates for a mixed finite element approximation of the Stokes equations , 1984 .
[39] Béatrice Rivière,et al. Discontinuous Galerkin methods for solving elliptic and parabolic equations - theory and implementation , 2008, Frontiers in applied mathematics.
[40] Alexander Linke,et al. On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime , 2014 .
[41] Jean-Frédéric Gerbeau,et al. Spurious velocities in the steady flow of an incompressible fluid subjected to external forces , 1997 .
[42] M. Olshanskii. A low order Galerkin finite element method for the Navier–Stokes equations of steady incompressible flow: a stabilization issue and iterative methods , 2002 .
[43] S. C. Brenner,et al. Forty Years of the Crouzeix‐Raviart element , 2015 .
[44] M. Fortin,et al. A stable finite element for the stokes equations , 1984 .
[45] Gunar Matthies,et al. Robust arbitrary order mixed finite element methods for the incompressible Stokes equations , 2014 .
[46] P Frolkovi,et al. Consistent Velocity Approximation for Density Driven Ow and Transport , 1998 .