Finite element approximation for fourth-order nonlinear problem in the plane

In this paper, a class of fourth-order nonlinear elliptic problem is investigated in a bounded convex domain Ω⊂R2. Under some assumptions, the existence and uniqueness of solution are proved via the Schaefer's Fixed Point Theorem. Furthermore, conforming finite element approximation is applied and H2-error estimate and L2-error estimate are obtained. Finally, the numerical experiments are provided to verify our theoretical analysis.