Abstract
The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.
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This research is supported by the National Natural Science Foundation of China under Grant Nos. 10671184 and 10971203.
This paper was recommended for publication by Editor Ningning YAN.
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Shi, D., Zhang, B. High accuracy analysis of the finite element method for nonlinear viscoelastic wave equations with nonlinear boundary conditions. J Syst Sci Complex 24, 795–802 (2011). https://doi.org/10.1007/s11424-011-8315-x
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DOI: https://doi.org/10.1007/s11424-011-8315-x