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Si, H.Y. and Chen, S.C. (2012) A New Mixed Finite Element Scheme for the Biharmonic Equation. Mathematica Numerica Sinica, 34, 173-182. (In Chinese)

has been cited by the following article:

• TITLE: Full Discrete Mixed Finite Element Method for the BBM Equation on a Rectangular Grid

  AUTHORS: Hongying Si, Weifeng Cui

  KEYWORDS: BBM Equation, The Mixed Finite Element, Full Discretization, Error Estimate

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.14 No.8, August 26, 2026

  ABSTRACT: In this paper, the mixed finite element method is applied to two-dimensional nonlinear BBM equations on rectangular meshes. The mixed finite element schemes of semidiscretization and full discretization are established. The space is approximated by a continuous biquadratic finite element and a bilinear finite element, and the time is discretized by the backward Euler difference scheme. The existence and uniqueness of the finite element solution are proved, and the optimal error estimation is obtained. Finally, the numerical results were given, and the stability and convergence of the method were verified.