Analysis of artificial dissipation of explicit and implicit time-integration methods
暂无分享,去创建一个
Hendrik Ranocha | Jan Glaubitz | Philipp Offner | Hendrik Ranocha | Philipp Öffner | J. Glaubitz | P. Öffner
[1] R. Abgrall,et al. High Order Schemes for Hyperbolic Problems Using Globally Continuous Approximation and Avoiding Mass Matrices , 2017, J. Sci. Comput..
[2] Aaas News,et al. Book Reviews , 1893, Buffalo Medical and Surgical Journal.
[3] Jan Nordström,et al. Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains , 2015, J. Comput. Phys..
[4] W. Marsden. I and J , 2012 .
[5] Hendrik Ranocha,et al. Enhancing stability of correction procedure via reconstruction using summation-by-parts operators I: Artificial dissipation , 2016 .
[6] Lisandro Dalcin,et al. Relaxation Runge-Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations , 2019, SIAM J. Sci. Comput..
[7] H. T. Huynh,et al. A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods , 2007 .
[8] Gregor Gassner,et al. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry , 2015, J. Comput. Phys..
[9] E. Tadmor,et al. Convergence of spectral methods for nonlinear conservation laws. Final report , 1989 .
[10] Carlos Lozano,et al. Entropy Production by Explicit Runge–Kutta Schemes , 2018, J. Sci. Comput..
[11] Heping Ma,et al. Chebyshev--Legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws , 1998 .
[12] E. Hairer,et al. Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .
[13] Rémi Abgrall,et al. Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes , 2019, J. Comput. Phys..
[14] Andrew J. Majda,et al. The Fourier method for nonsmooth initial data , 1978 .
[15] David C. Del Rey Fernández,et al. Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations , 2014 .
[16] Magnus Svärd,et al. Stable and Accurate Artificial Dissipation , 2004, J. Sci. Comput..
[17] Mengping Zhang,et al. STRONG STABILITY PRESERVING PROPERTY OF THE DEFERRED CORRECTION TIME DISCRETIZATION , 2008 .
[18] Philipp Öffner,et al. Extended skew-symmetric form for summation-by-parts operators and varying Jacobians , 2017, J. Comput. Phys..
[19] Philipp Öffner,et al. L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document} Stability of Explicit Runge–Kutta Schemes , 2017, Journal of Scientific Computing.
[20] N. SIAMJ.,et al. CHEBYSHEV – LEGENDRE SUPER SPECTRAL VISCOSITY METHOD FOR NONLINEAR CONSERVATION LAWS , 1998 .
[21] David I. Ketcheson,et al. Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms , 2019, SIAM J. Numer. Anal..
[22] Philipp Öffner,et al. Spectral convergence for orthogonal polynomials on triangles , 2013, Numerische Mathematik.
[23] Hendrik Ranocha,et al. Generalised summation-by-parts operators and variable coefficients , 2017, J. Comput. Phys..
[24] G. J. Cooper. Stability of Runge-Kutta Methods for Trajectory Problems , 1987 .
[25] Philipp Öffner,et al. Summation-by-parts operators for correction procedure via reconstruction , 2015, J. Comput. Phys..
[26] T. Sonar,et al. Enhancing stability of correction procedure via reconstruction using summation-by-parts operators II: Modal filtering , 2016, 1606.01056.
[27] Élise Le Mélédo,et al. On the Connection between Residual Distribution Schemes and Flux Reconstruction , 2018, 1807.01261.
[28] Jean-Luc Guermond,et al. Entropy viscosity method for nonlinear conservation laws , 2011, J. Comput. Phys..
[29] Philipp Öffner,et al. Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators , 2018, Applied Numerical Mathematics.
[30] Alberto Costa Nogueira,et al. Smooth and Compactly Supported Viscous Sub-cell Shock Capturing for Discontinuous Galerkin Methods , 2018, J. Sci. Comput..
[31] Jan Nordström,et al. A Roadmap to Well Posed and Stable Problems in Computational Physics , 2016, Journal of Scientific Computing.
[32] Jan Glaubitz,et al. Shock Capturing by Bernstein Polynomials for Scalar Conservation Laws , 2019, Appl. Math. Comput..
[33] J. S. Hesthaven,et al. Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method , 2011, 1102.3190.
[34] Hendrik Ranocha,et al. On strong stability of explicit Runge–Kutta methods for nonlinear semibounded operators , 2018, IMA Journal of Numerical Analysis.
[35] Chi-Wang Shu,et al. Stability of the fourth order Runge–Kutta method for time-dependent partial differential equations , 2017 .
[36] David I. Ketcheson,et al. Strong stability preserving runge-kutta and multistep time discretizations , 2011 .
[37] Jan Nordström,et al. Summation-by-parts in time , 2013, J. Comput. Phys..
[38] Philipp Öffner,et al. Application of modal filtering to a spectral difference method , 2016, Math. Comput..
[39] Eitan Tadmor,et al. Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems , 2003, Acta Numerica.
[40] Hendrik Ranocha,et al. Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods , 2016, GEM - International Journal on Geomathematics.
[41] Gregor Gassner,et al. A well balanced and entropy conservative discontinuous Galerkin spectral element method for the shallow water equations , 2016, Appl. Math. Comput..
[42] T. A. Zang,et al. Spectral Methods: Fundamentals in Single Domains , 2010 .
[43] T. Sonar,et al. Detecting Strength and Location of Jump Discontinuities in Numerical Data , 2013 .
[44] Eitan Tadmor,et al. From Semidiscrete to Fully Discrete: Stability of Runge-Kutta Schemes by The Energy Method , 1998, SIAM Rev..
[45] Gregor Gassner,et al. Entropy Stable Space–Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws , 2018, J. Sci. Comput..
[46] Chi-Wang Shu,et al. Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws , 2017, J. Comput. Phys..
[47] David I. Ketcheson,et al. Highly Efficient Strong Stability-Preserving Runge-Kutta Methods with Low-Storage Implementations , 2008, SIAM J. Sci. Comput..
[48] Hendrik Ranocha,et al. Some notes on summation by parts time integration methods , 2019, Results in Applied Mathematics.
[49] Philipp Öffner,et al. Error Boundedness of Discontinuous Galerkin Methods with Variable Coefficients , 2018, J. Sci. Comput..
[50] D. Gottlieb,et al. Spectral methods for hyperbolic problems , 2001 .
[51] Rémi Abgrall,et al. A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes , 2017, J. Comput. Phys..
[52] Rémi Abgrall,et al. Some Remarks About Conservation for Residual Distribution Schemes , 2017, Comput. Methods Appl. Math..
[53] David W. Zingg,et al. High-Order Implicit Time-Marching Methods Based on Generalized Summation-By-Parts Operators , 2014, SIAM J. Sci. Comput..
[54] Anne Gelb,et al. Using $$\ell _1$$ℓ1 Regularization to Improve Numerical Partial Differential Equation Solvers , 2018, J. Sci. Comput..
[55] Eitan Tadmor,et al. Arbitrarily High-order Accurate Entropy Stable Essentially Nonoscillatory Schemes for Systems of Conservation Laws , 2012, SIAM J. Numer. Anal..
[56] Chi-Wang Shu,et al. Total variation diminishing Runge-Kutta schemes , 1998, Math. Comput..
[57] Steven H. Frankel,et al. Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces , 2014, SIAM J. Sci. Comput..
[58] Hendrik Ranocha,et al. Stability of correction procedure via reconstruction with summation-by-parts operators for Burgers' equation using a polynomial chaos approach , 2017, ESAIM: Mathematical Modelling and Numerical Analysis.
[59] H. Kreiss,et al. Time-Dependent Problems and Difference Methods , 1996 .
[60] Philipp Offner,et al. Error boundedness of Correction Procedure via Reconstruction / Flux Reconstruction , 2018, 1806.01575.
[61] Eitan Tadmor,et al. The numerical viscosity of entropy stable schemes for systems of conservation laws. I , 1987 .
[62] Zheng Sun,et al. Strong Stability of Explicit Runge-Kutta Time Discretizations , 2018, SIAM J. Numer. Anal..
[63] Carlos Lozano,et al. Entropy Production by Implicit Runge–Kutta Schemes , 2019, J. Sci. Comput..
[64] Anne Gelb,et al. High Order Edge Sensors with ℓ1 Regularization for Enhanced Discontinuous Galerkin Methods , 2019, SIAM J. Sci. Comput..
[65] R. D. Richtmyer,et al. A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .