In this paper,the high accuracy analysis of an energy-stable fully discrete finite element(FE)scheme for the Benjamin-Bona-Mahony-Burgers(BBMB)equation is studied.Firstly,the stability of energy of backward-Euler(B-E)fully discrete scheme is proved which leads to the boundedness of the FE solution in H1-norm.Secondly,the existence and uniqueness of solution for approximation problem are proved by employing the above boundedness and Brouwer fixed-point theorem.Thirdly,by use of the special property of bilinear element,the superclose and global su-perconvergence results are derived.Finally,a numerical test is given to verify the validity of the theoretical analysis.
BBMB equationenergy-stable schemesuperclose and superconvergence analysis
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