Journal
APPLIED MATHEMATICS LETTERS
Volume 84, Issue -, Pages 34-41Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2018.04.012
Keywords
Superclose and superconvergence results; TGM; Semilinear parabolic equations; Galerkin FEMs
Categories
Funding
- National Natural Science Foundation of China [11671369, 11271340]
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In this paper, the superconvergence analysis of a two-grid method (TGM) is established for the semilinear parabolic equations. Based on the combination of the interpolation and Ritz projection technique, an important ingredient in the method, the superclose estimates in the H-1-norm are deduced for the backward Euler fully discrete TGM scheme. Moreover, through the interpolated postprocessing approach, the corresponding global superconvergence result is derived. Finally, some numerical results are provided to confirm the theoretical analysis, and also show that the computing cost of the proposed TGM is only half of the conventional Galerkin finite element methods (FEMs). (C) 2018 Elsevier Ltd. All rights reserved.
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