1.Adjerid, S., Baccouch, M.:A superconvergent local discontinuous Galerkin method for elliptic problems.J.Sci.Comput.52, 113-152 (2012)
2.Adjerid, S., Chaabane, N.:An improved superconvergence error estimate for the LDG method.Appl.Numer.Math.98, 122-136 (2015)
3.Arnold, D.N.:An interior penalty fnite element method with discontinuous elements.SIAM J.Numer.Anal.39, 742-760 (1982)
4.Baccouch, M.:A superconvergent local discontinuous Galerkin method for the second-order wave equation on Cartesian grids.Comput.Math.Appl.68, 1250-1278 (2014)
5.Baccouch, M.:Superconvergence of the local discontinuous Galerkin method for the sine-Gordon equation on Cartesian grids.Appl.Numer.Math.113, 124-155 (2017)
6.Baccouch, M.:Optimal error estimates of the local discontinuous Galerkin method for the two-dimensional sine-Gordon equation on Cartesian grids.Int.J.Numer.Anal.Model.16, 436-462 (2019)
7.Baccouch, M.:Analysis of a local discontinuous Galerkin method for nonlinear second-order elliptic problems on Cartesian grids.J.Numer.Methods Partial Difer.Equ.37, 505-532 (2021)
8.Baccouch, M.:Optimal superconvergence and asymptotically exact a posteriori error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids.Appl.Numer.Math.162, 201-224 (2021)
9.Baccouch, M., Adjerid, S.:A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-difusion problems.J.Sci.Comput.62, 399-430 (2014)
10.Bank, R.E., Li, Y.:Superconvergent recovery of Raviart-Thomas mixed fnite elements on triangular grids.J.Sci.Comput.81(3), 1882-1905 (2019)
11.Bank, R.E., Xu, J.:Asymptotically exact a posteriori error estimators, part I:grids with superconvergence.SIAM J.Numer.Anal.41(6), 2294-2312 (2003)
12.Bassi, F., Rebay, S.:A high-order accurate discontinuous fnite element method for the numerical solution of the compressible Navier-Stokes equations.J.Comput.Phys.131, 267-279 (1997)
13.Baumann, C.E., Oden, J.T.:A discontinuous hp fnite element method for convection-difusion problems.Comput.Methods Appl.Mech.Eng.175, 311-341 (1999)
14.Berestycki, H., de Figueiredo, D.G.:Double resonance in semilinear elliptic problems.Commun.Partial Difer.Equ.6(1), 91-120 (1981)
15.Bramble, J.H., Xu, J.:A local post-processing technique for improving the accuracy in mixed fniteelement approximations.SIAM J.Numer.Anal.26(6), 1267-1275 (1989)
16.Brandts, J.H.:Superconvergence and a posteriori error estimation for triangular mixed fnite elements.Numerische Mathematik 68(3), 311-324 (1994)
17.Brandts, J.H.:Superconvergence for triangular order k=1 Raviart-Thomas mixed fnite elements and for triangular standard quadratic fnite element methods.Appl.Numer.Math.34(1), 39-58 (2000)
18.Bustinza, R., Gatica, G.N.:A local discontinuous Galerkin method for nonlinear difusion problems with mixed boundary conditions.SIAM J.Sci.Comput.26, 152-177 (2004)
19.Castillo, P.:An optimal estimate for the local discontinuous Galerkin method.In:Cockburn, B., Karniadakis, G.E., Shu, C.-W.(eds.) Discontinuous Galerkin Methods.Lecture Notes in Computational Science and Engineering, vol.11, pp.285-290.Springer, Berlin (2000)
20.Castillo, P.:A review of the local discontinuous Galerkin (LDG) method applied to elliptic problems.Appl.Numer.Math.56, 1307-1313 (2006)
21.Castillo, P., Cockburn, B., Perugia, I., Schötzau, D.:An a priori error analysis of the local discontinuous Galerkin method for elliptic problems.SIAM J.Numer.Anal.38, 1676-1706 (2000)
22.Castillo, P., Cockburn, B., Schötzau, D., Schwab, C.:Optimal a priori error estimates for the hp-version of the local discontinuous Galerkin method for convection-difusion problems.Math.Comput.71, 455-478 (2002)
23.Chen, A., Li, F., Cheng, Y.:An ultra-weak discontinuous Galerkin method for Schrödinger equation in one dimension.J.Sci.Comput.78(2), 772-815 (2019)
24.Chen, C., Huang, Y.Q.:High accuracy theory of fnite element methods.Hunan Science and Technology Press, Changsha (1995)
25.Chen, H., Li, B.:Superconvergence analysis and error expansion for the Wilson nonconforming fnite element.Numerische Mathematik 69(2), 125-140 (1994)
26.Ciarlet, P.G.:The Finite Element Method for Elliptic Problems.SIAM, New Delhi (2002)
27.Ciarlet, P.G.:Linear and Nonlinear Functional Analysis with Applications.SIAM, Philadelphia (2013)
28.Cockburn, B.:Discontinuous Galerkin methods for computational fuid dynamics.In:Stein, E., de Borst, R., Hughes, T.J.R.(eds.) Encyclopedia of Computational Mechanics (2nd Edition), pp.1-63.John Wiley & Sons, Inc.(2018)
29.Cockburn, B., Dawson, C.:Some extensions of the local discontinuous Galerkin method for convection-difusion equations in multidimensions.In:The Mathematics of Finite Elements and Applications, X, MAFELAP 1999 (Uxbridge), pp.225-238.Elsevier, Oxford (2000)
30.Cockburn, B., Fu, G.:Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions.IMA J.Numer.Anal.38(2), 566-604 (2018)
31.Cockburn, B., Gopalakrishnan, J., Guzmán, J.:A new elasticity element made for enforcing weak stress symmetry.Math.Comput.79(271), 1331-1349 (2010)
32.Cockburn, B., Guzmán, J., Wang, H.:Superconvergent discontinuous Galerkin methods for secondorder elliptic problems.Math.Comput.78(265), 1-24 (2009)
33.Cockburn, B., Kanschat, G., Perugia, I., Schötzau, D.:Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids.SIAM J.Numer.Anal.39, 264-285 (2001)
34.Cockburn, B., Kanschat, G., Schötzau, D.:A locally conservative LDG method for the incompressible Navier-Stokes equations.Math.Comput.74, 1067-1095 (2004)
35.Cockburn, B., Kanschat, G., Schötzau, D.:The local discontinuous Galerkin method for linearized incompressible fuid fow:a review.Comput.Fluids 34(4/5), 491-506 (2005)
36.Cockburn, B., Karniadakis, G.E., Shu, C.-W.:Discontinuous Galerkin Methods Theory, Computation and Applications.Lecture Notes in Computational Science and Engineering, vol.11.Springer, Berlin (2000)
37.Cockburn, B., Qiu, W., Shi, K.:Conditions for superconvergence of HDG methods for second-order elliptic problems.Math.Comput.81(279), 1327-1353 (2012)
38.Cockburn, B., Shi, K.:Superconvergent HDG methods for linear elasticity with weakly symmetric stresses.IMA J.Numer.Anal.33(3), 747-770 (2013)
39.Cockburn, B., Shu, C.-W.:The local discontinuous Galerkin method for time-dependent convection-difusion systems.SIAM J.Numer.Anal.35, 2440-2463 (1998)
40.Cockburn, B., Shu, C.-W.:Runge-Kutta discontinuous Galerkin methods for convection-dominated problems.J.Sci.Comput.16(3), 173-261 (2001)
41.Degond, P., Liu, H., Savelief, D., Vignal, M.H.:Numerical approximation of the Euler-PoissonBoltzmann model in the quasineutral limit.J.Sci.Comput.51(1), 59-86 (2012)
42.Douglas, J., Wang, J.:Superconvergence of mixed fnite element methods on rectangular domains.Calcolo 26(2), 121-133 (1989)
43.Durán, R., Nochetto, R., Wang, J.P.:Sharp maximum norm error estimates for fnite element approximations of the Stokes problem in 2-D.Math.Comput.51(184), 491-506 (1988)
44.Gilbarg, D., Trudinger, N.S.:Elliptic Partial Diferential Equations of Second Order.Springer, Berlin (2015)
45.Glowinski, R.:Variational Methods for the Numerical Solution of Nonlinear Elliptic Problems.SIAM, New Delhi (2015)
46.Gopalakrishnan, J., Guzmán, J.:A second elasticity element using the matrix bubble.IMA J.Numer.Anal.32(1), 352-372 (2012)
47.Gudi, T., Nataraj, N., Pani, A.:An hp-local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type.Math.Comput.77, 731-756 (2008)
48.Hille, B.:Ionic Channels of Excitable Membranes.Sinauer Associates, Sunderland (1984)
49.Hu, J., Ma, L., Ma, R.:Optimal superconvergence analysis for the Crouzeix-Raviart and the Morley elements.arXiv:1808.09810 (2018)
50.Hu, J., Ma, R.:Superconvergence of both the Crouzeix-Raviart and Morley elements.Numerische Mathematik 132(3), 491-509 (2016)
51.Liu, H., Yan, J.:The direct discontinuous Galerkin (DDG) methods for difusion problems.SIAM J.Numer.Anal.47, 675-698 (2009)
52.Reed, W.H., Hill, T.R.:Triangular mesh methods for the neutron transport equation.Tech.Rep.LA-UR-73-479, Los Alamos Scientifc Laboratory, Los Alamos (1991)
53.Shu, C.-W.:Discontinuous Galerkin methods:general approach and stability.In:Bertoluzza, S., Falletta, S., Russo, G., Shu, C.-W.(eds.) Numerical Solutions of Partial Diferential Equations.Advanced Courses in Mathematics, pp.149-201.CRM, Barcelona (2009)
54.Shu, C.-W.:Discontinuous Galerkin method for time-dependent problems:survey and recent developments.In:Feng, X., Karakashian, O., Xing, Y.(eds.) Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Diferential Equations.The IMA Volumes in Mathematics and its Applications, vol.157, pp.25-62.Springer, Cham (2014)
55.Stenberg, R.:Postprocessing schemes for some mixed fnite elements.ESAIM:Mathematical Modelling and Numerical Analysis 25(1), 151-167 (1991) 476 Communications on Applied Mathematics and Computation (2022) 4:437-476 1 3
56.Troy, W.C.:Symmetry properties in systems of semilinear elliptic equations.J.Difer.Equ.42(3), 400-413 (1981)
57.Wheeler, M.F.:An elliptic collocation-fnite element method with interior penalties.SIAM J.Numer.Anal.15, 152-161 (1978)
58.Xie, Z., Zhang, Z., Zhang, Z.:A numerical study of uniform superconvergence of LDG method for solving singularly perturbed problems.J.Comput.Math.27(2/3), 280-298 (2009)
59.Xu, Y., Shu, C.-W.:Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection-difusion and KdV equations.Comput.Methods Appl.Mech.Eng.196, 3805-3822 (2007)
60.Xu, Y., Shu, C.-W.:Local discontinuous Galerkin methods for high-order time-dependent partial differential equations.Commun.Comput.Phys.7, 1-46 (2010)
61.Yadav, S., Pani, A.K.:Superconvergence of a class of expanded discontinuous Galerkin methods for fully nonlinear elliptic problems in divergence form.J.Comput.Appl.Math.333, 215-234 (2018)
62.Yadav, S., Pani, A.K., Park, E.J.:Superconvergent discontinuous Galerkin methods for nonlinear elliptic equations.Math.Comput.82, 1297-1335 (2013)
