1. Adjerid, S., Devine, K.D., Flaherty, J.E., Krivodonova, L.: A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems. Comput. Methods Appl. Mech. Eng. 191(11), 1097–1112 (2002)
2. Adjerid, S, Issaev, D.: Superconvergence of the local discontinuous Galerkin method applied to diffusion problems. In: Proceedings of the Third MIT Conference on Computational Fluid and Solid Mechanics, vol.
3, pp. 1040–1042. Elsevier, Boston, MA (2005) 3. Adjerid, S., Massey, T.C.: Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem. Comput. Methods Appl. Mech. Eng. 195(25), 3331–3346 (2006)
4. Brenner, S.C.: Poincaré-Friedrichs inequalities for piecewise H1 functions. SIAM J. Numer. Anal. 41(1), 306–324 (2003)
5. Cao, W., Li, D., Yang, Y., Zhang, Z.: Superconvergence of discontinuous Galerkin methods based on upwind-biased fluxes for 1D linear hyperbolic equations. ESAIM Math. Model. Numer. Anal. 51(2), 467–486 (2017)
6. Cao, W., Shu, C.-W., Yang, Y., Zhang, Z.: Superconvergence of discontinuous Galerkin methods for two-dimensional hyperbolic equations. SIAM J. Numer. Anal. 53(4), 1651–1671 (2015)
7. Cao, W., Shu, C.-W., Yang, Y., Zhang, Z.: Superconvergence of discontinuous Galerkin method for scalar nonlinear hyperbolic equations. SIAM J. Numer. Anal. 56(2), 732–765 (2018)
8. Cao, W., Shu, C.-W., Zhang, Z.M.: Superconvergence of discontinuous Galerkin methods for 1-D linear hyperbolic equations with degenerate variable coefficients. ESAIM: Math. Model. Numer. Anal. 51(6), 2213–2235 (2017)
9. Cao, W., Zhang, Z., Zou, Q.: Superconvergence of discontinuous Galerkin methods for linear hyperbolic equations. SIAM J. Numer. Anal. 52(5), 2555–2573 (2014)
10. Chen, A., Cheng, Y., Liu, Y., Zhang, M.: Superconvergence of ultra-weak discontinuous Galerkin methods for the linear Schrödinger equation in one dimension. J. Sci. Comput. 82(1), 22 (2020)
11. Cheng, Y., Shu, C.-W.: A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives. Math. Comput. 77(262), 699–730 (2008)
12. Cheng, Y., Shu, C.-W.: Superconvergence and time evolution of discontinuous Galerkin finite element solutions. J. Comput. Phys. 227(22), 9612–9627 (2008)
13. Cheng, Y., Shu, C.-W.: Superconvergence of local discontinuous Galerkin methods for one-dimensional convection-diffusion equations. Comput. Struct. 87(11/12), 630–641 (2009)
14. Cheng, Y., Shu, C.-W.: Superconvergence of discontinuous Galerkin and local discontinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension. SIAM J. Numer. Anal. 47(6), 4044–4072 (2010)
15. Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convectiondiffusion systems. SIAM J. Numer. Anal. 35(6), 2440–2463 (1998)
16. Dong, B., Shu, C.-W.: Analysis of a local discontinuous Galerkin method for linear time-dependent fourth-order problems. SIAM J. Numer. Anal. 47(5), 3240–3268 (2009)
17. Ji, L., Xu, Y.: Optimal error estimates of the local discontinuous Galerkin method for Willmore flow of graphs on Cartesian meshes. Int. J. Numer. Anal. Model. 8(2), 252–283 (2011)
18. Liu, H., Yan, J.: A local discontinuous Galerkin method for the Korteweg-de Vries equation with boundary effect. J. Comput. Phys. 215(1), 197–218 (2006)
19. Liu, Y., Shu, C.-W., Zhang, M.: Superconvergence of energy-conserving discontinuous Galerkin methods for linear hyperbolic equations. Commun. Appl. Math. Comput. 1(1), 101–116 (2019)
20. Liu, Y., Tao, Q., Shu, C.-W.: Analysis of optimal superconvergence of an ultraweak-local discontinuous Galerkin method for a time dependent fourth-order equation. ESAIM: Math. Model. Numer. Anal. 54(6),1797–1820 (2020)
21. Tao, Q., Cao, W., Zhang, Z.: Superconvergence analysis of the ultra-weak local discontinuous Galerkin method for one dimensional linear fifth order equations. J. Sci. Comput. 88(3), 63 (2021)
22. Tao, Q., Xu, Y.: Superconvergence of arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for linear hyperbolic equations. SIAM J. Numer. Anal. 57(5), 2142–2165 (2019)
23. Tao, Q., Xu, Y., Shu, C.-W.: An ultraweak-local discontinuous Galerkin method for PDEs with high order spatial derivatives. Math. Comput. 89(326), 2753–2783 (2020)
24. Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for high-order time-dependent partial differential equations. Commun. Comput. Phys. 7(1), 1 (2010)
25. Yan, J., Shu, C.-W.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40(2), 769–791 (2002)
26. Yan, J., Shu, C.-W.: Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. J. Sci. Comput. 17, 27–47 (2002)
27. Zhong, W.X.: On precise integration method. J. Comput. Appl. Math. 163(1), 59–78 (2004)