Analysis of a linearization scheme for an interior penalty discontinuous Galerkin method for two‐phase flow in porous media with dynamic capillarity effects
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[1] Andreas Dedner,et al. A generic grid interface for parallel and adaptive scientific computing. Part I: abstract framework , 2008, Computing.
[2] Andreas Dedner,et al. A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE , 2008, Computing.
[3] Mary F. Wheeler,et al. A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems , 2001, SIAM J. Numer. Anal..
[4] A. Ern,et al. Mathematical Aspects of Discontinuous Galerkin Methods , 2011 .
[5] Iuliu Sorin Pop,et al. Two-phase porous media flows with dynamic capillary effects and hysteresis: Uniqueness of weak solutions , 2015, Comput. Math. Appl..
[6] Luca Bergamaschi,et al. MIXED FINITE ELEMENTS AND NEWTON-TYPE LINEARIZATIONS FOR THE SOLUTION OF RICHARDS' EQUATION , 1999 .
[7] Buyang Li,et al. Maximum-norm stability and maximal $$L^{p}$$Lp regularity of FEMs for parabolic equations with Lipschitz continuous coefficients , 2013, Numerische Mathematik.
[8] William G. Gray,et al. Thermodynamic basis of capillary pressure in porous media , 1993 .
[9] Jan M. Nordbotten,et al. Geological Storage of CO2: Modeling Approaches for Large-Scale Simulation , 2011 .
[10] F. Radu,et al. Mixed finite elements for the Richards' equation: linearization procedure , 2004 .
[11] Florin A. Radu,et al. Mixed finite element discretization and Newton iteration for a reactive contaminant transport model with nonequilibrium sorption: convergence analysis and error estimates , 2011 .
[12] J. Hesthaven,et al. On the constants in hp-finite element trace inverse inequalities , 2003 .
[13] I. Pop,et al. Degenerate two-phase porous media flow model with dynamic capillarity , 2016 .
[14] W. Yong,et al. A Numerical Approach To Porous Medium Equations , 1996 .
[15] M. Celia,et al. A General Mass-Conservative Numerical Solution for the Unsaturated Flow Equation , 1990 .
[16] B. Rivière,et al. Analysis of hp discontinuous Galerkin methods for incompressible two-phase flow , 2009 .
[17] Olaf Ippisch,et al. Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase , 2012, Computational Geosciences.
[18] Eun-Jae Park,et al. Mixed finite element methods for nonlinear second-order elliptic problems , 1995 .
[19] Marián Slodicka,et al. A Robust and Efficient Linearization Scheme for Doubly Nonlinear and Degenerate Parabolic Problems Arising in Flow in Porous Media , 2001, SIAM J. Sci. Comput..
[20] Stefan Karpinski,et al. Analysis of an interior penalty discontinuous Galerkin scheme for two phase flow in porous media with dynamic capillary effects , 2017, Numerische Mathematik.
[21] Michael A. Celia,et al. Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow , 2002 .
[22] Carlota M. Cuesta,et al. Numerical schemes for a pseudo-parabolic Burgers equation : discontinuous data and long-time behaviour , 2009 .
[23] David A. DiCarlo,et al. Experimental measurements of saturation overshoot on infiltration , 2004 .
[24] R. Helmig. Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems , 2011 .
[25] F. Radu,et al. A study on iterative methods for solving Richards’ equation , 2015, Computational Geosciences.
[26] S. Kräutle,et al. The semismooth Newton method for multicomponent reactive transport with minerals , 2011 .
[27] Michael A. Celia,et al. Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow , 2002 .
[28] François Lehmann,et al. Comparison of Iterative Methods for Improved Solutions of the Fluid Flow Equation in Partially Saturated Porous Media , 1998 .
[29] H. Diersch,et al. Modeling Unsaturated Flow in Absorbent Swelling Porous Media: Part 1. Theory , 2010 .
[30] Shuyu Sun,et al. A new treatment of capillarity to improve the stability of IMPES two-phase flow formulation , 2010 .
[31] Alexandre Ern,et al. Discrete functional analysis tools for Discontinuous Galerkin methods with application to the incompressible Navier-Stokes equations , 2010, Math. Comput..
[32] Spencer J. Sherwin,et al. Stability of Projection Methods for Incompressible Flows Using High Order Pressure-Velocity Pairs of Same Degree: Continuous and Discontinuous Galerkin Formulations , 2014 .
[33] Shuyu Sun,et al. ON ITERATIVE IMPES FORMULATION FOR TWO-PHASE FLOW WITH CAPILLARITY IN HETEROGENEOUS POROUS MEDIA , 2010 .
[34] S. M. Hassanizadeh,et al. A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media , 2001 .
[35] Jan M. Nordbotten,et al. A robust linearization scheme for finite volume based discretizations for simulation of two-phase flow in porous media , 2015, J. Comput. Appl. Math..
[36] J. Nordbotten,et al. A convergent mass conservative numerical scheme based on mixed finite elements for two-phase flow in porous media , 2015, 1512.08387.
[37] CH' , 2018, Dictionary of Upriver Halkomelem.
[38] Mary F. Wheeler,et al. L∞-boundedness of the finite element galerkin operator for parabolic problems , 1982 .
[39] BEN SCHWEIZER,et al. Two-phase flow equations with a dynamic capillary pressure , 2012, European Journal of Applied Mathematics.
[40] Peter Knabner,et al. Newton—Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations , 2006 .
[41] Peter Bastian,et al. Generic implementation of finite element methods in the Distributed and Unified Numerics Environment (DUNE) , 2010, Kybernetika.