CONVERGENCE  RATE ESTIMATES

A collection of selected references on

Piecewise regularity and convergence rate estimates
for nonlinear transport equations

• E. Tadmor (1991) [pdf file]
  Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
  SIAM Journal Numerical Analysis 28 (1991) 891-906.
  
  
• H. Nessyahu & E. Tadmor (1992) [pdf file]
  The convergence rate of approximate solutions for nonlinear scalar conservation laws
  SIAM Journal Numerical Analysis 29 (1991) 1505-1519.
  
  
• E. Tadmor & T. Tassa (1993) [pdf file]
  On the piecewise smoothness of entropy solutions to scalar conservation laws
  Communications on Partial Differential Equations 18 (1993) 1631-1652.
  
  
• E. Tadmor (1993) [pdf file]
  Total variation and error estimates for spectral viscosity approximations
  Mathematics of Computation 60 (1993) 245-256.
  
• B. Cockburn, F. Coquel & P. LeFloch (1994) [pdf file]
  An error estimate for finite volume methods for multidimensional conservation laws
  Mathematics of Computations 63 (1994) 77-103.
  
  

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• H. Nessyahu, E. Tadmor & T. Tassa (1994) [pdf file]
  The convergence rate of Godunov type schemes
  SIAM Journal Numerical Analysis 31 (1994) 1-16.
  
  
• H. Nessyahu & T. Tassa  (1994) [pdf file]
  Convergence rate of approximate solutions to conservation laws with initial rarefacrtions
  SIAM Journal Numerical Analysis 31 (1994) 628-654.
  
  
• H. Nessyahu (1996) [pdf file]
  Convergence rate of approximate solutions to weakly coupled nonlinear systems
  Mathematics of Computation 65 (1996) 575-585-342.
  
  
• A. Kurganov & E. Tadmor (1997) [pdf file]
  Stiff systems of hyperbolic conservation laws: convergence and error estimates
  SIAM Journal of Mathematical Analysis 28 (1997) 1446-1456.
  
  
• F. James (1998) [pdf file]
  Convergence results for some conservation laws with a reflux boundary condition and a relaxation term arising in chemical engineering
  SIAM Journal of Mathematical Analysis 29 (1998) 1200-1223.
  
  

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• E. Tadmor & T. Tang (1998) [pdf file]
  Pointwise convergence rate for nonlinear conservation laws
  Hyperbolic Problems:Theory, Numerics, Applications Proceedings of the 7th int'l Conference in Zurich, Feb. 1998 (M. Fey and R. Jeltsch, eds.), Birkhauser ISNM v. 130 (1999) pp. 925-934.
  
  
• W. -C. Wang (1998) [pdf file]
  On L¹ convergence rate of viscous and numerical approximate solutions of genuinely nonlinear scalar conservation laws
  SIAM Journal of Mathematical Analysis 30 (1998) 38-52.
  
  
• W. Shen, A. Tveito & R. Winther (1999) [pdf file]
  On the zero relaxation limit for a system modeling the motion of viscoelastic solid
  SIAM Journal of Mathematical Analysis 30 (1999) 1115-1135.
  
  
• E. Tadmor & T. Tang (1999) [pdf file]
  Pointwise error estimates for scalar conservation laws with piecewise smooth solutions
  SIAM Journal Numerical Analysis 36 (1999) 1739-1758.
  
  
• E. Tadmor & T. Tang (2000) [pdf file]
  Pointwise error estimates for relaxation approximations to conservation laws
  SIAM Journal Mathematical Analysis 32 (2000) 870-886.
  
  

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• C.-T. Lin & E. Tadmor (2000) [pdf file]
  High-resolution non oscillatory central schemes for Hamilton-Jacobi equations
  SIAM Journal of Scientific Computations 21 (2000) 2163-2186.
  
  
• L. Gosse & C. Makridakis (2000) [pdf file]
  Two a posteriori error estimates for one-dimensional scalar conservation laws
  SIAM Journal Numerical Analysis 38 (2000) 964-988.
  
  
• T. Tang (2000) [pdf file]
  Error estimates for approximate solutions for nonlinear scalar conservation laws
  "Hyperbolic Problems: Theory, Numerics, Applications", Proceedings of the 8th international conference held in Magdeburg, (H. Freistuhler and G. Warnecke, eds.), v. 141, Birkhauser, 873-882.
  
  
• T. Tang & J. Wang (2000) [pdf file]
  Convergence of MUSCL relaxing schemes to the relaxed schemes of conservation laws with stiff source terms
  Journal of Scientific Computing 15 (2000) 173-195.
  
  
• H. Liu,  J. Wang & G. Warnecke (2001) [pdf file]
  The Lip⁺ stability and error estimates for a relaxation scheme
  SIAM Journal Numerical Analysis 38 (2001) 1154-1170.
  
  

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• H. Liu, J. Wang & G. Warnecke (2001) [pdf file]
  Convergence of a splitting scheme applied to the Ruijgrok-Wu model of the Boltzmann equation
  Journal of Computational and Applied mathematics 134 (2001)  343-367.
  
  
• Y.-X. Kan, T.Tang & Z.-H. Teng (2001) [pdf file]
  On the piecewise smooth solutions to non-homogeneous scalar conservation laws
  Journal of Differential Equations 175 (2001) 27-50.
  
  
• C. T. Lin & E. Tadmor (2001) [pdf file]
  L¹-stability and error estimates for approximate Hamilton-Jacobi solutions
  Numerische Mathematik 87 (2001) 701-735.
  
  
• G. Petrova & B. Popov (2001) [gzipped  file]
  Linear transport equations with discontinuous coefficients
  
  
• T. Tang & Z.-H. Teng (2001) [pdf file]
  On the regularity of approximate solutions to conservation laws with piecewise smooth solutions
  SIAM Journal Numerical Analysis 38 (2001) 1483-1495.
  
  

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• H. Berestycki, S. Kamin & G. Sivashinsky (2001) [pdf file]
  Metastability in a flame front evolution equation
  Interfaces and Free Boundaries 3 (2001) 361-392.
  
  
• L. Gosse & F. James (2002) [pdf file]
  Convergence results for an inhomogeneous  system arising in various high frequency approximations
  Numerische Mathematik 90 (2002) 721-753.
  
  
• S. Karni, A. Kurganov  & G. Petrova (2002) [pdf file]
  Smoothness indicators for adaptive algorithms
  Journal of Computational Physics 178 (2002) 323-341.
  
  
• A, J, Briggs, J. R. Claisse & C. M. Elliott (2002) [pdf file]
  Finite-difference approximation of a one-dimensional Hamilton-Jacobi system arising in superconductivity
  IMA Journal of Numerocal Analysis 22 (2002) 89-131.
  
  
• T. Tang, Z.-H. Teng & Z.-P. Xin   [gzipped file]
  Fractional rate of convergence for viscous approximation to non-convex conservation laws .
  
  
• C. Chainais-Hillairet & S. Champier   [gzipped file]
  Finite volume schemes for non-homogeneous scalar conservation laws: error estimates
  Numerische Mathematik 88(4) (2001) 607-639
  
  
• S. Karni & A. Kurganov [zipped file]
  Local error analysis for approximate solutions of hyperbolic conservation laws
  Advances in Computational Mathematics 22 (2005), 79-99
  
  
• J.-H. Wang & H. Zhang [pdf file]
  Existence and decay rate of solutions to the generalized Burgers equations
  
  
• M. Kuther [pdf file]
  A priori error estimates for approximate solutions to convex conservation laws
  Numerische Mathematik 93 (2003) 697-728.
  
  

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