Abstract
In this paper, we investigate the superconvergence criteria of the discontinuous Galerkin (DG) method applied to one-dimensional nonlinear differential equations. We show numerically that the p-degree finite element (DG) solution is \(O(\Delta x^{p+2})\) superconvergent at the roots of specific combined Jacobi polynomials. Moreover, we used these results to construct efficient and asymptotically exact a posteriori error estimates.
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Acknowledgements
We acknowledge the Gulf University for Science and Technology (GUST) for partially supporting this research in terms of conference grants.
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Temimi, H. (2016). Superconvergence of Discontinuous Galerkin Method to Nonlinear Differential Equations. In: Chen, K., Ravindran, A. (eds) Forging Connections between Computational Mathematics and Computational Geometry. Springer Proceedings in Mathematics & Statistics, vol 124. Springer, Cham. https://doi.org/10.5176/2251-1911_CMCGS14.24_4
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DOI: https://doi.org/10.5176/2251-1911_CMCGS14.24_4
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