Abstract
AbstractIn this paper, an energy-stable Crank–Nicolson fully discrete finite element scheme is proposed for the Benjamin–Bona–Mahony–Burgers equation. Firstly, the stability of energy is proved, which leads to the boundedness of the finite element solution in $H^{1}$
H
1
-norm. Secondly, combining with the above boundedness and the special property of bilinear element, the unconditional superclose and superconvergence results are derived. Finally, numerical examples are provided to illustrate the validity and efficiency of our theoretical analysis and method.
Funder
Innovative Research Group Project of the National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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