On error estimates for Galerkin finite element methods for the Camassa-Holm equation.
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V. A. Dougalis | D. E. Mitsotakis | D. C. Antonopoulos | V. Dougalis | D. Antonopoulos | D. Mitsotakis
[1] P. Olver,et al. Well-posedness and Blow-up Solutions for an Integrable Nonlinearly Dispersive Model Wave Equation , 2000 .
[2] Hongjun Gao,et al. An initial boundary value problem of Camassa–Holm equation , 2000 .
[3] L. R. Scott,et al. Numerical schemes for a model for nonlinear dispersive waves , 1985 .
[4] Xavier Raynaud,et al. A convergent numerical scheme for the Camassa--Holm equation based on multipeakons , 2005 .
[5] A. Constantin,et al. Orbital stability of solitary waves for a shallow water equation , 2001 .
[6] B. Fuchssteiner. Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation , 1996 .
[7] Jian-Guo Liu,et al. Convergence of a Particle Method and Global Weak Solutions of a Family of Evolutionary PDEs , 2012, SIAM J. Numer. Anal..
[8] J. Douglas,et al. Optimal _{∞} error estimates for Galerkin approximations to solutions of two-point boundary value problems , 1975 .
[9] F. Smith,et al. Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.
[10] J. Escher,et al. Wave breaking for nonlinear nonlocal shallow water equations , 1998 .
[11] Finite Element Methods of High-Order Accuracy for Singular Two-Point Boundary Value Problems with Nonsmooth Solutions , 1980 .
[12] Darryl D. Holm,et al. A New Integrable Shallow Water Equation , 1994 .
[13] Pascal Redou,et al. On the Inverse Scattering Approach to the Camassa-Holm Equation , 2003, math-ph/0403039.
[14] Kenneth H. Karlsen,et al. A Convergent Finite Difference Scheme for the Camassa-Holm Equation with General H1 Initial Data , 2008, SIAM J. Numer. Anal..
[15] A. Parker. Wave dynamics for peaked solitons of the Camassa–Holm equation , 2008 .
[16] R. Johnson,et al. On solutions of the Camassa-Holm equation , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[17] J. Escher,et al. Global existence and blow-up for a shallow water equation , 1998 .
[18] Allen Parker,et al. On the Camassa-Holm equation and a direct method of solution I. Bilinear form and solitary waves , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[19] Xavier Raynaud,et al. Convergence of a Finite Difference Scheme for the Camassa-Holm Equation , 2006, SIAM J. Numer. Anal..
[20] A. Constantin,et al. The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations , 2007, 0709.0905.
[21] Xavier Raynaud,et al. Convergence of a spectral projection of the Camassa‐Holm equation , 2006 .
[22] A. Fokas. On a class of physically important integrable equations , 1994 .
[23] Yan Xu,et al. A Local Discontinuous Galerkin Method for the Camassa-Holm Equation , 2008, SIAM J. Numer. Anal..
[24] L. Molinet. On Well-Posedness Results for Camassa-Holm Equation on the Line: A Survey , 2004 .
[25] HAILIANG LIU,et al. An Invariant Preserving Discontinuous Galerkin Method for the Camassa-Holm Equation , 2016, SIAM J. Sci. Comput..
[26] J. Lenells. Traveling wave solutions of the Camassa-Holm equation , 2005 .
[27] Athanassios S. Fokas,et al. Symplectic structures, their B?acklund transformation and hereditary symmetries , 1981 .
[28] Robert Artebrant,et al. Numerical simulation of Camassa-Holm peakons by adaptive upwinding , 2006 .
[29] R. Johnson,et al. Camassa–Holm, Korteweg–de Vries and related models for water waves , 2002, Journal of Fluid Mechanics.
[30] W. Strauss,et al. Stability of peakons , 2000 .
[31] Allen Parker,et al. On the Camassa–Holm equation and a direct method of solution. III. N-soliton solutions , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[32] H. Kalisch,et al. Numerical study of traveling-wave solutions for the Camassa-Holm equation , 2005 .
[33] Alina Chertock,et al. Elastic collisions among peakon solutions for the Camassa-Holm equation , 2015 .
[34] Joachim Escher,et al. Initial Boundary Value Problems of the Camassa–Holm Equation , 2008 .
[35] A. Bressan,et al. Global Conservative Solutions of the Camassa–Holm Equation , 2007 .
[36] D. C. Antonopoulos,et al. Numerical solution of Boussinesq systems of the Bona--Smith family , 2010 .
[37] C. D. Boor,et al. Spline approximation by quasiinterpolants , 1973 .
[38] A. Constantin. On the Cauchy Problem for the Periodic Camassa–Holm Equation , 1997 .
[39] Adrian Constantin,et al. Stability of the Camassa-Holm solitons , 2002, J. Nonlinear Sci..
[40] Darryl D. Holm,et al. An integrable shallow water equation with peaked solitons. , 1993, Physical review letters.
[41] J. Douglas,et al. Optimal Lœ Error Estimates for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems , 2010 .
[42] Rolf Rannacher,et al. Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations , 1982 .
[43] V. Thomée,et al. Maximum-norm stability and error estimates in Galerkin methods for parabolic equations in one space variable , 1983 .
[44] Allen Parker,et al. On the Camassa–Holm equation and a direct method of solution. II. Soliton solutions , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[45] A. Constantin. On the scattering problem for the Camassa-Holm equation , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[46] J. Bona,et al. Model equations for long waves in nonlinear dispersive systems , 1972, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.
[47] Vidar Thomée,et al. Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems , 1974 .