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.