Abstract
Previous finite element analysis about the nonlinear degenerate wave equation mainly focused on convergence based on regular meshes. Recently, superconvergence based on anisotropic mesh has become a hot topic in finite element analysis. In this paper, convergence analysis of the bilinear finite element method to a kind of nonlinear degenerate wave equation on anisotropic meshes is considered. Moreover, the global superconvergence for semidiscrete scheme is proposed through interpolation instead of the Ritz Volterra projection of the exact solution, which makes the proof rather simpler than the previous studies.
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Li, Z., Liu, L., Qu, J., Cui, Y. (2010). Superconvergence Analysis of Anisotropic Finite Element Method for a Kind of Nonlinear Degenerate Wave Equation. In: Zhu, R., Zhang, Y., Liu, B., Liu, C. (eds) Information Computing and Applications. ICICA 2010. Communications in Computer and Information Science, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16339-5_45
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DOI: https://doi.org/10.1007/978-3-642-16339-5_45
Publisher Name: Springer, Berlin, Heidelberg
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