Numerical methods for conservation laws

Keywords: methodes : numeriques ; lois : conservatives ; Euler : equation d' Reference Record created on 2005-11-18, modified on 2016-08-08

[1]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[2]  J. Burgers A mathematical model illustrating the theory of turbulence , 1948 .

[3]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[4]  P. Lax Hyperbolic systems of conservation laws II , 1957 .

[5]  Nicholas Chako,et al.  Wave propagation and group velocity , 1960 .

[6]  O. Oleinik Discontinuous solutions of non-linear differential equations , 1963 .

[7]  G. Strang Accurate partial difference methods I: Linear cauchy problems , 1963 .

[8]  Gilbert Strang,et al.  Accurate partial difference methods , 1964 .

[9]  L. Carleson On convergence and growth of partial sums of Fourier series , 1966 .

[10]  J. Fromm A method for reducing dispersion in convective difference schemes , 1968 .

[11]  M. Ronald Wohlers,et al.  I – Linear Systems , 1969 .

[12]  W. McCulloch Of I and It , 2015 .

[13]  R. Geroch,et al.  The domain of dependence , 1970 .

[14]  J. Cole,et al.  Calculation of plane steady transonic flows , 1970 .

[15]  J. L. Lions,et al.  3. Nonlinear Systems , 1972 .

[16]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme I. The quest of monotonicity , 1973 .

[17]  W. H. Reed,et al.  Triangular mesh methods for the neutron transport equation , 1973 .

[18]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[19]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[20]  P. Raviart,et al.  On a Finite Element Method for Solving the Neutron Transport Equation , 1974 .

[21]  R. F. Warming,et al.  The modified equation approach to the stability and accuracy analysis of finite-difference methods , 1974 .

[22]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme. II. Monotonicity and conservation combined in a second-order scheme , 1974 .

[23]  B. Fornberg On a Fourier method for the integration of hyperbolic equations , 1975 .

[24]  David L. Book,et al.  Flux-corrected transport II: Generalizations of the method , 1975 .

[25]  R. F. Warming,et al.  An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. [application to Eulerian gasdynamic equations , 1976 .

[26]  N. N. Kuznetsov Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation , 1976 .

[27]  Alexandre J. Chorin,et al.  Random choice solution of hyperbolic systems , 1976 .

[28]  R. F. Warming,et al.  Upwind Second-Order Difference Schemes and Applications in Aerodynamic Flows , 1976 .

[29]  J. Boris,et al.  Flux-corrected transport. III. Minimal-error FCT algorithms , 1976 .

[30]  THE WAVE EQUATION , 1976 .

[31]  Joseph Oliger,et al.  Stability of the Fourier method , 1977 .

[32]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme III. Upstream-centered finite-difference schemes for ideal compressible flow , 1977 .

[33]  B. Vanleer,et al.  Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection , 1977 .

[34]  Peter D. Lax,et al.  Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations , 1978 .

[35]  Peter D. Lax,et al.  The computation of discontinuous solutions of linear hyperbolic equations , 1978 .

[36]  Andrew J. Majda,et al.  The Fourier method for nonsmooth initial data , 1978 .

[37]  S. Zalesak Fully multidimensional flux-corrected transport algorithms for fluids , 1979 .

[38]  M. Crandall,et al.  Monotone difference approximations for scalar conservation laws , 1979 .

[39]  S. Osher,et al.  Numerical viscosity and the entropy condition , 1979 .

[40]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[41]  C. Brezinski Padé-type approximation and general orthogonal polynomials , 1980 .

[42]  F. Stenger Numerical Methods Based on Whittaker Cardinal, or Sinc Functions , 1981 .

[43]  David Gottlieb,et al.  Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives , 1981 .

[44]  B. Vanleer,et al.  On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe , 1984 .

[45]  S. Osher,et al.  One-sided difference approximations for nonlinear conservation laws , 1981 .

[46]  G. D. van Albada,et al.  A comparative study of computational methods in cosmic gas dynamics , 1982 .

[47]  G. Chavent,et al.  A finite-element method for the 1-D water flooding problem with gravity , 1982 .

[48]  A. Quarteroni,et al.  Approximation results for orthogonal polynomials in Sobolev spaces , 1982 .

[49]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[50]  S. Osher Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[51]  J. Falcovitz,et al.  A second-order Godunov-type scheme for compressible fluid dynamics , 1984 .

[52]  P. Woodward,et al.  The Piecewise Parabolic Method (PPM) for Gas Dynamical Simulations , 1984 .

[53]  P. Sweby High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws , 1984 .

[54]  Sukumar Chakravarthy,et al.  High Resolution Schemes and the Entropy Condition , 1984 .

[55]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[56]  B. Lucier Error Bounds for the Methods of Glimm, Godunov and LeVeque , 1985 .

[57]  P. Colella A Direct Eulerian MUSCL Scheme for Gas Dynamics , 1985 .

[58]  G. Páris,et al.  The Gibbs phenomenon in generalized Padé approximation , 1985 .

[59]  S. Osher,et al.  Some results on uniformly high-order accurate essentially nonoscillatory schemes , 1986 .

[60]  C. Basdevant,et al.  Spectral and finite difference solutions of the Burgers equation , 1986 .

[61]  P. Roe CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[62]  Matania Ben-Artzi,et al.  Application of the “generalized Riemann problem” method to 1-D compressible flows with material interfaces , 1986 .

[63]  S. Osher,et al.  Very High Order Accurate TVD Schemes , 1986 .

[64]  Juhani Pitkäranta,et al.  An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation , 1986 .

[65]  E. Tadmor The exponential accuracy of Fourier and Chebyshev differencing methods , 1986 .

[66]  E. Tadmor,et al.  Convergence of spectral methods for nonlinear conservation laws. Final report , 1989 .

[67]  Peter Albrecht,et al.  A new theoretical approach to Runge-Kutta methods , 1987 .

[68]  Eitan Tadmor,et al.  The numerical viscosity of entropy stable schemes for systems of conservation laws. I , 1987 .

[69]  J. Boris,et al.  The numerical simulation of compressible reactive flows , 1987 .

[70]  H. C. Yee,et al.  Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates , 1987 .

[71]  Chi-Wang Shu TVB uniformly high-order schemes for conservation laws , 1987 .

[72]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[73]  E. Tadmor Stability analysis of finite-difference, pseudospectral and Fourier-Galerkin approximations for time-dependent problems , 1987 .

[74]  Walter Noll,et al.  Finite-Dimensional Spaces , 1987 .

[75]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .

[76]  Eduard Harabetian,et al.  Rarefactions and large time behavior for parabolic equations and monotone schemes , 1988 .

[77]  G. Richter An Optimal-Order Error Estimate for the Discontinuous Galerkin Method , 1988 .

[78]  D. Gottlieb,et al.  A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations , 1988 .

[79]  H. C. Yee,et al.  A class of high resolution explicit and implicit shock-capturing methods , 1989 .

[80]  ShuChi-Wang,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes, II , 1989 .

[81]  Phillip Colella,et al.  Higher order Godunov methods for general systems of hyperbolic conservation laws , 1989 .

[82]  Guy Chavent,et al.  The local projection P 0 − P 1 -discontinuous-Galerkin finite element method for scalar conservation laws , 2009 .

[83]  B. E. McDonald,et al.  Flux-corrected pseudospectral method for scalar hyperbolic conservation laws , 1989 .

[84]  E. Tadmor,et al.  Analysis of the spectral vanishing viscosity method for periodic conservation laws , 1989 .

[85]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[86]  Chi-Wang Shu,et al.  TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems , 1989 .

[87]  Chi-Wang Shu Numerical experiments on the accuracy of ENO and modified ENO schemes , 1990 .

[88]  E. Tadmor,et al.  Non-oscillatory central differencing for hyperbolic conservation laws , 1990 .

[89]  Eitan Tadmor,et al.  Shock capturing by the spectral viscosity method , 1990 .

[90]  P. Colella Multidimensional upwind methods for hyperbolic conservation laws , 1990 .

[91]  Eckart Meiburg,et al.  A numerical study of the convergence properties of ENO schemes , 1990 .

[92]  Bernardo Cockburn,et al.  The Runge-Kutta local projection discontinous Galerkin finite element method for conservation laws , 1990 .

[93]  Chi-Wang Shu,et al.  The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case , 1990 .

[94]  D. Gottlieb,et al.  The CFL condition for spectral approximations to hyperbolic initial-boundary value problems. , 1991 .

[95]  Hervé Vandeven,et al.  Family of spectral filters for discontinuous problems , 1991 .

[96]  A. Staniforth,et al.  Semi-Lagrangian integration schemes for atmospheric models - A review , 1991 .

[97]  Chi-Wang Shu,et al.  The Runge-Kutta local projection $P^1$-discontinuous-Galerkin finite element method for scalar conservation laws , 1988, ESAIM: Mathematical Modelling and Numerical Analysis.

[98]  Todd E. Peterson,et al.  A note on the convergence of the discontinuous Galerkin method for a scalar hyperbolic equation , 1991 .

[99]  Daniele,et al.  CONVERGENCE RESULTS FOR PSEUDOSPECTRAL APPROXIMATIONS OF HYPERBOLIC SYSTEMS BY A PENALTY TYPE BOUNDARY TREATMENT , 1991 .

[100]  J. Kraaijevanger Contractivity of Runge-Kutta methods , 1991 .

[101]  Tayfan E. Tezduyar,et al.  Stabilized Finite Element Formulations for Incompressible Flow Computations , 1991 .

[102]  Michael E. Taylor,et al.  Propagation of singularities , 1991 .

[103]  Alex Solomonoff,et al.  On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function , 1992 .

[104]  George Em Karniadakis,et al.  Spectral element‐FCT method for scalar hyperbolic conservation laws , 1992 .

[105]  Z. Xin,et al.  Viscous limits for piecewise smooth solutions to systems of conservation laws , 1992 .

[106]  Catherine Mavriplis,et al.  Adaptive mesh strategies for the spectral element method , 1992 .

[107]  Yvon Maday,et al.  Polynomial interpolation results in Sobolev spaces , 1992 .

[108]  R D Richtmyek,et al.  Survey of the Stability of Linear Finite Difference Equations , 2022 .