Shi, Dong-Yang; Tang, Qi-Li Nonconforming \(H^{1}\)-Galerkin mixed finite element method for strongly damped wave equations. (English) Zbl 1284.65138 Numer. Funct. Anal. Optim. 34, No. 12, 1348-1369 (2013). The authors study the superconvergence analysis of the nonconforming \(H^{1}\)-Galerkin mixed finite element method for strongly damped wave equations under almost uniform meshes. Numerical results are discussed to confirm the theoretical results. Reviewer: Răzvan Răducanu (Iaşi) Cited in 10 Documents MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35L70 Second-order nonlinear hyperbolic equations 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs Keywords:damped wave equation; \(H^{1}\)-Galerkin mixed scheme; nonconforming finite elements; superconvergence; almost uniform meshes; numerical results PDFBibTeX XMLCite \textit{D.-Y. Shi} and \textit{Q.-L. Tang}, Numer. Funct. Anal. Optim. 34, No. 12, 1348--1369 (2013; Zbl 1284.65138) Full Text: DOI References: [1] DOI: 10.1016/0010-4655(77)90009-1 · doi:10.1016/0010-4655(77)90009-1 [2] Clarkson P. A., Stud. in Appl. Math. 75 pp 95– (1986) · Zbl 0606.73028 · doi:10.1002/sapm198675295 [3] DOI: 10.1063/1.864487 · Zbl 0544.76170 · doi:10.1063/1.864487 [4] DOI: 10.1007/BF01396752 · Zbl 0631.65107 · doi:10.1007/BF01396752 [5] DOI: 10.1007/BF01389710 · Zbl 0599.65072 · doi:10.1007/BF01389710 [6] Johnson C., RAIRO Numer. Anal. 15 pp 41– (1981) · Zbl 0476.65074 · doi:10.1051/m2an/1981150100411 [7] DOI: 10.1016/0045-7825(90)90165-I · Zbl 0724.65087 · doi:10.1016/0045-7825(90)90165-I [8] Geveci T., Math. Model. Numer. Anal. 22 pp 243– (1988) · Zbl 0646.65083 · doi:10.1051/m2an/1988220202431 [9] Brezzi F., RAIRO Modél. Math. Anal. Numér. 21 pp 129– (1974) [10] DOI: 10.1007/978-1-4612-3172-1 · Zbl 0788.73002 · doi:10.1007/978-1-4612-3172-1 [11] DOI: 10.1007/978-3-642-61623-5 · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5 [12] DOI: 10.1137/S0036142995280808 · Zbl 0915.65107 · doi:10.1137/S0036142995280808 [13] Pani A. K., Int. J. Numer. Anal. Model. 1 pp 111– (2004) [14] DOI: 10.1002/num.20431 · Zbl 1425.65094 · doi:10.1002/num.20431 [15] Chen H. Z., Int. J. Numer. Anal. Model. 9 pp 132– (2012) [16] Che H. T., Math. Probl. Eng. 570980 pp 10– (2011) [17] DOI: 10.1007/s00607-005-0158-7 · Zbl 1098.65096 · doi:10.1007/s00607-005-0158-7 [18] DOI: 10.1016/j.amc.2009.02.039 · Zbl 1178.65119 · doi:10.1016/j.amc.2009.02.039 [19] DOI: 10.1016/j.apm.2009.11.007 · Zbl 1195.65136 · doi:10.1016/j.apm.2009.11.007 [20] Liu Y., Math. Numer. Sinica 32 pp 157– (2010) [21] DOI: 10.1007/s10255-007-7065-y · Zbl 1187.65131 · doi:10.1007/s10255-007-7065-y [22] DOI: 10.1080/01630563.2011.602202 · Zbl 1253.65173 · doi:10.1080/01630563.2011.602202 [23] DOI: 10.1080/00036810903208163 · Zbl 1179.65118 · doi:10.1080/00036810903208163 [24] Chen S. C., Acta Math. Sci. Ser. B. 20 pp 44– (2000) [25] Yan N. N., Superconvergence Analysis and A Posteriori Error Estimation in Finite Element Methods (2008) [26] Shi D. Y., J. Comput. Math. 27 pp 299– (2009) [27] DOI: 10.1093/imanum/drh008 · Zbl 1068.65122 · doi:10.1093/imanum/drh008 [28] X. B. Hao , D. W. Shi , and D. Y. Shi ( 2011 ). Special convergence analysis of quasi-Wilson element. Multimedia Technology (ICMT), 2011 International Conference on, July pp. 6016–6018. [29] Shi D. Y., J. Comput. Math. 24 pp 561– (2006) [30] Shi Z. C., Math. Numer. Sinica 8 pp 159– (1986) [31] DOI: 10.1002/num.1690080202 · Zbl 0742.76051 · doi:10.1002/num.1690080202 [32] DOI: 10.1007/s10444-007-9054-3 · Zbl 1180.65140 · doi:10.1007/s10444-007-9054-3 [33] DOI: 10.1080/00207160.2010.534138 · Zbl 1241.65103 · doi:10.1080/00207160.2010.534138 [34] DOI: 10.1007/PL00005466 · doi:10.1007/PL00005466 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.