We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition arising from a natural minimisation formulation allows to get an optimal a priori error estimate for the finite element scheme improving the existing error estimate for such a formulation without weakly imposed Dirichlet boundary condition. We also briefly outline the algebraic formulation arising from the finite element method.

翻译：我们考虑一种基于双正交系统且弱施加Dirichlet边界条件的混合有限元方法，用于求解带夹紧边界条件的双调和方程。研究表明，由自然极小化公式产生的弱施加边界条件能够为该有限元方案获得最优先验误差估计，从而改进了现有未采用弱施加Dirichlet边界条件的此类公式的误差估计。此外，我们简要概述了由该有限元方法导出的代数公式。