Zienkiewicz-Type Finite Element Applied to Fourth-Order Problems

In general, a finite element method (FEM) for fourth-order problems requires trial and test functions belonging to subspaces of the Sobolev space H2(Ω), and this would require C1−elements, i.e., piecewise polynomials which are C1 across interelement boundaries In order to avoid this requirement we will use nonconforming Zienkiewicz-type (Z-type) triangle applied to biharmonic problem We propose a new approach to prove the order of convergence by comparison to suitable modified Hermite triangular finite element This method is more natural and it could be also applied to the corresponding fourth-order eigenvalue problem Some computational aspects are discussed and numerical example is given.