Free Access
Issue
ESAIM: M2AN
Volume 46, Number 3, May-June 2012
Special volume in honor of Professor David Gottlieb
Page(s) 545 - 557
DOI https://doi.org/10.1051/m2an/2011050
Published online 11 January 2012
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  2. M. Ainsworth, Dispersive and dissipative behavior of high-order discontinuous Galerkin finite element methods. J. Comput. Phys. 198 (2004) 106–130. [CrossRef]
  3. D. Appelö and T. Hagstrom, Experiments with Hermite methods for simulating compressible flows : Runge-Kutta time-stepping and absorbing layers, in 13th AIAA/CEAS Aeroacoustics Conference. AIAA (2007).
  4. G. Birkhoff, M. Schultz and R. Varga, Piecewise Hermite interpolation in one and two variables with applications to partial differential equations. Numer. Math. 11 (1968) 232–256. [CrossRef] [MathSciNet]
  5. P. Borwein and T. Erdélyi, Polynomials and Polynomial Inequalities. Springer-Verlag, New York (1995).
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  7. L. Demkowicz, J. Kurtz, D. Pardo, M. Paszynski, W. Rachowicz and A. Zdunek, Computing with hp-Adaptive Finite Elements. Applied Mathematics & Nonlinear Science, Chapman & Hall/CRC, Boca Raton (2007).
  8. C. Dodson, A high-order Hermite compressible Navier-Stokes solver. Master’s thesis, The University of New Mexico (2003).
  9. B. Fornberg, On a Fourier method for the integration of hyperbolic equations. SIAM J. Numer. Anal. 12 (1975) 509–528. [CrossRef] [MathSciNet]
  10. J. Goodrich, T. Hagstrom and J. Lorenz, Hermite methods for hyperbolic initial-boundary value problems. Math. Comput. 75 (2006) 595–630.
  11. D. Gottlieb and S.A. Orszag, Numerical Analysis of Spectral Methods. SIAM, Philadelphia (1977).
  12. D. Gottlieb and E. Tadmor, The CFL condition for spectral approximations to hyperbolic initial-boundary value problems. Math. Comput. 56 (1991) 565–588. [CrossRef]
  13. A. Griewank, Evaluating Derivatives : Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia (2000).
  14. E. Hairer, C. Lubich and M. Schlichte, Fast numerical solution of nonlinear Volterra convolutional equations. SIAM J. Sci. Statist. Comput. 6 (1985) 532–541. [CrossRef] [MathSciNet]
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  17. F. Lörcher, G. Gassner and C.-D. Munz, An explicit discontinuous Galerkin scheme with local time-stepping for general unsteady diffusion equations. J. Comput. Phys. 227 (2008) 5649–5670. [CrossRef]
  18. T. Warburton and T. Hagstrom, Taming the CFL number for discontinuous Galerkin methods on structured meshes. SIAM J. Numer. Anal. 46 (2008) 3151–3180. [CrossRef] [MathSciNet]
  19. J. Weideman and L. Trefethen, The eigenvalues of second-order differentiation matrices. SIAM J. Numer. Anal. 25 (1988) 1279–1298. [CrossRef] [MathSciNet]

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