A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation

Xiangyu Shi and Linzhang Lu

Applied Mathematics and Computation, 2020, vol. 371, issue C

Abstract: A new low order two-grid mixed finite element method (FEM) is developed for the nonlinear Benjamin-Bona-Mahoney (BBM) equation, in which the famous nonconforming rectangular CNQ1rot element and Q0 × Q0 constant element are used to approximate the exact solution u and the variable p→=∇ut, respectively. Then, based on the special properties of these two elements and interpolation post-processing technique, the superconvergence results for u in broken H1-norm and p→ in L2-norm are obtained for the semi-discrete and Crank-Nicolson fully-discrete schemes without the restriction between the time step τ and coarse mesh size H or the fine mesh size h, which improve the results of the existing literature. Finally, some numerical results are provided to confirm the theoretical analysis.

Keywords: BBM equation; Nonconforming finite element; Two-grid mixed FEM; Semi-discrete and Crank-Nicolson fully-discrete schemes; Unconditional superconvergence behavior (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:371:y:2020:i:c:s009630031930935x

DOI: 10.1016/j.amc.2019.124943

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