Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics
暂无分享,去创建一个
[1] Albert Y. Zomaya,et al. Partial Differential Equations , 2007, Explorations in Numerical Analysis.
[2] Charalambos Makridakis,et al. A Posteriori Analysis of Discontinuous Galerkin Schemes for Systems of Hyperbolic Conservation Laws , 2014, SIAM J. Numer. Anal..
[3] J. Giesselmann,et al. Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics , 2014, 1405.4776.
[4] C. Rohde,et al. A low-order approximation for viscous-capillary phase transition dynamics , 2013 .
[5] Yan Xu,et al. A Local Discontinuous Galerkin Method for the Propagation of Phase Transition in Solids and Fluids , 2013, Journal of Scientific Computing.
[6] J. Giesselmann. Low Mach asymptotic-preserving scheme for the Euler–Korteweg model , 2013, 1308.6177.
[7] J. Giesselmann,et al. Energy consistent discontinuous Galerkin methods for a quasi-incompressible diffuse two phase flow model , 2013, 1307.8248.
[8] M. Braack,et al. Stable discretization of a diffuse interface model for liquid-vapor flows with surface tension , 2013 .
[9] Yulong Xing,et al. Conservative, discontinuous Galerkin-methods for the generalized Korteweg-de Vries equation , 2013, Math. Comput..
[10] Charalambos Makridakis,et al. Energy consistent discontinuous Galerkin methods for the Navier-Stokes-Korteweg system , 2012, Math. Comput..
[11] A. Ern,et al. Mathematical Aspects of Discontinuous Galerkin Methods , 2011 .
[12] Chi-Wang Shu,et al. Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation , 2011 .
[13] Omar Lakkis,et al. A Posteriori Error Control for Discontinuous Galerkin Methods for Parabolic Problems , 2008, SIAM J. Numer. Anal..
[14] Chi-Wang Shu,et al. A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives , 2007, Math. Comput..
[15] Endre Süli,et al. Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems , 2007, SIAM J. Numer. Anal..
[16] Ricardo H. Nochetto,et al. A posteriori error analysis for higher order dissipative methods for evolution problems , 2006, Numerische Mathematik.
[17] Charalambos Makridakis,et al. Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations , 2004, Math. Comput..
[18] Zhangxin Chen,et al. Pointwise Error Estimates of Discontinuous Galerkin Methods with Penalty for Second-Order Elliptic Problems , 2004, SIAM J. Numer. Anal..
[19] Ohannes A. Karakashian,et al. A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems , 2003, SIAM J. Numer. Anal..
[20] Ricardo H. Nochetto,et al. Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems , 2006, Math. Comput..
[21] D. J. Torres,et al. On the theory and computation of surface tension: the elimination of parasitic currents through energy conservation in the second-gradient method , 2002 .
[22] P. LeFloch,et al. Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves , 2002 .
[23] Philippe G. Ciarlet,et al. The finite element method for elliptic problems , 2002, Classics in applied mathematics.
[24] M. Thanh,et al. Non-classical Riemann solvers and kinetic relations. II. An hyperbolic–elliptic model of phase-transition dynamics , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.
[25] O. Lebaigue,et al. The second gradient method for the direct numerical simulation of liquid—vapor flows with phase change , 2001 .
[26] C. Chalons,et al. High-order entropy-conservative schemes and kinetic relations for van der Waals fluids , 2001 .
[27] Philippe G. LeFloch,et al. Nonclassical Shocks and Kinetic Relations: Strictly Hyperbolic Systems , 2000, SIAM J. Math. Anal..
[28] C. Dafermos. Hyberbolic Conservation Laws in Continuum Physics , 2000 .
[29] C. Makridakis. Finite element approximations of nonlinear elastic waves , 1993 .
[30] J. K. Knowles,et al. Kinetic relations and the propagation of phase boundaries in solids , 1991 .
[31] M. Slemrod. Admissibility criteria for propagating phase boundaries in a van der Waals fluid , 1983 .
[32] J. Ball,et al. Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity , 1982 .
[33] M. Slemrod. Dynamic phase transitions in a van der Waals fluid , 1981 .
[34] C. Dafermos. The second law of thermodynamics and stability , 1979 .
[35] R. J. Diperna. Uniqueness of Solutions to Hyperbolic Conservation Laws. , 1978 .
[36] Jan Giesselmann,et al. A relative entropy approach to convergence of a low order approximation to a nonlinear elasticity model with viscosity and capillarity Jan Giesselmann , 2014 .
[37] C. Makridakis,et al. Error Control for Discontinuous Galerkin Methods for First Order Hyperbolic Problems , 2014 .
[38] A. Bressan. Hyperbolic Systems of Conservation Laws , 1999 .
[39] Carlos Alberto Brebbia,et al. Applications to Partial Differential Equations , 1995 .
[40] N. Pavel. Nonlinear Evolution Operators and Semigroups , 1987 .