Abstract
In this paper, we briefly review some recent developments in the superconvergence of three types of discontinuous Galerkin (DG) methods for time-dependent partial differential equations: the standard DG method, the local discontinuous Galerkin method, and the direct discontinuous Galerkin method. A survey of our own results for various time-dependent partial differential equations is presented and the superconvergence phenomena of the aforementioned three types of DG solutions are studied for: (i) the function value and derivative approximation at some special points, (ii) cell average error and supercloseness.
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Waixiang Cao: Research supported in part by NSFC Grant No. 11501026, and and the Fundamental Research Funds for the Central Universities No. 2017NT10. Zhimin Zhang: Research supported in part by the following grants: NSFC 1147103 and 91430216, NSAF1530401, and NSF DMS-1419040.
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Cao, W., Zhang, Z. Some Recent Developments in Superconvergence of Discontinuous Galerkin Methods for Time-Dependent Partial Differential Equations. J Sci Comput 77, 1402–1423 (2018). https://doi.org/10.1007/s10915-018-0762-2
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DOI: https://doi.org/10.1007/s10915-018-0762-2