Publications in Refereed Journals (Appeared or Accepted)
Y. Xu, The convergence and stability of difference solutions for Burgers-KdV equation (in Chinese), Journal of Tianjin Normal University (Natural Science Edition), 22 (2002), pp.33-37.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for three classes of nonlinear wave equations, Journal of Computational Mathematics, 22 (2004), pp.250-274.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for nonlinear Schrodinger equations , Journal of Computational Physics, 205 (2005), pp.72-97.
Y. Xu, The convergence and stability of difference solutions for a class of coupled KdV equation (in Chinese), Journal of Engineering Mathematics, 22(2005), pp.47-52.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for two classes of two dimensional nonlinear wave equations , Physica D, 208 (2005), pp.21-58.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations , Computer Methods in Applied Mechanics and Engineering, 195 (2006), pp. 3430-3447.
Y. Xu and C.-W. Shu, Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-diffusion and KdV equations, Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp.3805-3822.
J.J.W. van der Vegt and Y. Xu, Space-time discontinuous Galerkin method for nonlinear water waves, Journal of Computational Physics, 224 (2007), pp.17-39.
Y. Xia, Y. Xu and C.-W. Shu, Efficient time discretization for local discontinuous Galerkin methods, Discrete and Continuous Dynamical Systems - Series B, 8 (2007), pp. 677-693.
Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Cahn-Hilliard type equations, Journal of Computational Physics, 227 (2007), pp. 472-491.
Y. Xu and C.-W. Shu, A local discontinuous Galerkin method for the Camassa-Holm equation, SIAM Journal on Numerical Analysis, 46 (2008), pp.1998-2021.
Y. Xu, J.J.W. van der Vegt and O. Bokhove, Discontinuous Hamiltonian finite element method for bilinear Poisson brackets, Journal of Scientific Computing, 35 (2008), pp.241-265.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for the Hunter-Saxton equation and its zero-viscosity and zero-dispersion limit, SIAM Journal on Scientific Computing, 31 (2008), pp. 1249-1268
Y. Xia, Y. Xu and C.-W. Shu, Application of the local discontinuous Galerkin method for the Allen-Cahn/Cahn-Hilliard system, Communications in Computational Physics, 5 (2009), pp. 821-835.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin method for surface diffusion and Willmore flow of graphs, Journal of Scientific Computing, 40 (2009), pp.375-390.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for high-order time-dependent partial differential equations, Communications in Computational Physics, 7 (2010), pp. 1-46.
Y. Xia, Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the generalized Zakharov system, Journal of Computational Physics, 229(2010), pp.1238-1259.
Y. Xu and C.-W. Shu, Dissipative numerical methods for the Hunter-Saxton equation , Journal of Computational Mathematics, 28(2010), pp.606-620.
L. Ji and Y. Xu, Optimal error estimates of the local discontinuous Galerkin method for Willmore flow of graphs on Cartesian meshes, International Journal of Numerical Analysis & Modeling, to appear.
Y. Xu and C.-W. Shu, Local discontinuous Galerkin methods for the Degasperis-Procesi equation, Communications in Computational Physics, to appear.
Publications in Refereed Proceedings
Y. Xu and C.-W. Shu, Preliminary results in local discontinuous Galerkin methods for two classes of 2D nonlinear wave equations (Abstract), in Abstracts of the Papers Presented at the Minisymposia Sessions of the Sixth World Congress on Computational Mechanics in conjunction with the Second Asian-Pacific Congress on Computational Mechanics, Z.H. Yao, M.W. Yuan and W.X. Zhong, editors, Tsinghua University Press Springer, 2004, p.212.
Y. Xu and J.J.W. van der Vegt, Space-time discontinuous Galerkin method for large amplitude nonlinear water waves, Computational Fluid Dynamics 2006: Proceedings of the Fourth International Conference on Computational Fluid Dynamics, ICCFD, Ghent, Belgium, July 10-14, 2006, H. Deconinck and E. Dick, (Eds.), Springer, 2009, pp. 53-58.
Preprint
L. Ji and Y. Xu, Optimal error estimates of the local discontinuous Galerkin method for surface diffusion of graphs on Cartesian meshes, submitted to SIAM Journal on Numerical Analysis.