Abstract
We unify the formulation and analysis of Galerkin and Runge–Kutta methods for the time discretization of parabolic equations. This, together with the concept of reconstruction of the approximate solutions, allows us to establish a posteriori superconvergence estimates for the error at the nodes for all methods.
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Georgios Akrivis was partially supported by the Institute of Applied and Computational Mathematics, FORTH, Greece. Charalambos Makridakis was partially supported by the RTN-network HYKE, HPRN-CT-2002-00282, the EU Marie Curie Dev. Host Site, HPMD-CT-2001-00121 and the program Pythagoras of EPEAEK II. Ricardo H. Nochetto was partially supported by NSF grants DMS-0505454 and DMS-0807811.
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Akrivis, G., Makridakis, C. & Nochetto, R.H. Galerkin and Runge–Kutta methods: unified formulation, a posteriori error estimates and nodal superconvergence. Numer. Math. 118, 429–456 (2011). https://doi.org/10.1007/s00211-011-0363-6
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DOI: https://doi.org/10.1007/s00211-011-0363-6