A Stable Mixed Element Method for the Biharmonic Equation with First-Order Function Spaces.

This paper studies the mixed element method for the boundary value problem of the biharmonic equation ▵²u = f in two dimensions. We start from a u ∼ ▿ ∼ ²u ∼ div ²u formulation that is discussed in [4] and construct its stability on H¹ ₀(Ω) × H¹ ₀(Ω) × L² _sym(Ω) × H^-1(div). Then we utilise the Helmholtz decomposition of H-1(div,Ω) and construct a new formulation stable on first-order and zero-order Sobolev spaces. Finite element discretisations are then given with respect to the new formulation, and both theoretical analysis and numerical verification are given. [ABSTRACT FROM AUTHOR]