The Hessian Discretisation Method for Fourth Order Linear Elliptic Equations

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Nonconforming tetrahedral finite elements for fourth order elliptic equations

This paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed elements include two nonconforming tetrahedral finite elements and one quasi-conforming tetrahedral element. These elements are proved to be convergent for a model biharmonic equation in three...

Concentration Phenomena for Fourth-order Elliptic Equations with Critical Exponent

We consider the nonlinear equation ∆u = u n+4 n−4 − εu with u > 0 in Ω and u = ∆u = 0 on ∂Ω. Where Ω is a smooth bounded domain in Rn, n ≥ 9, and ε is a small positive parameter. We study the existence of solutions which concentrate around one or two points of Ω. We show that this problem has no solutions that concentrate around a point of Ω as ε approaches 0. In contrast to this, we construct ...

SOME n - RECTANGLE NONCONFORMING ELEMENTS FOR FOURTH ORDER ELLIPTIC EQUATIONS

Motivated by both theoretical and practical interests, we will consider n-rectangle (n ≥ 2) nonconforming finite elements for n-dimensional fourth order partial equations in this paper. In the two dimensional case, there are well-known nonconforming elements, such as the Morley element, the Zienkiewicz element and the Adini element, etc (see [1-4]). In a recent paper [10], we have discussed the...

Bifurcation Problem for Biharmonic Asymptotically Linear Elliptic Equations

In this paper, we investigate the existence of positive solutions for the ellipticequation $Delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $Omega$ of $R^{n}$, $ngeq2$, with Navier boundary conditions. We show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...