hp-version interior penalty DGFEMs for the biharmoni equation Igor Mozolevski1, and Endre S uli2 We onstru t hp-version interior penalty dis ontinuous Galerkin nite element methods (DGFEMs) for the biharmoni equation, in luding symmetri and nonsymmetri interior penalty dis ontinuous Galerkin methods and their ombinations: semisymmetri methods. Our main on ern is to establish the stability and ...

The Powell–Sabin (PS) piecewise quadratic C finite element on the PS 12-split of a triangulation is a common choice for the construction of a BPX-type preconditioner for the biharmonic equation. In this note we investigate the related Powell–Sabin element on the PS 6-split instead of the PS 12-split for the construction of such preconditioners. For the PS 6-split element multilevel spaces can b...

A 2p-times continuously differentiable complex-valued function f = u+ iv in a simply connected domainΩ ⊆ C is p-harmonic if f satisfies the p-harmonic equation ∆p f = 0. In this paper, we investigate the properties of p-harmonic mappings in the unit disk |z| < 1. First, we discuss the convexity, the starlikeness and the region of variability of some classes of p-harmonic mappings. Then we prove...

In this paper, we first split the biharmonic equation !2u = f with nonhomogeneous essential boundary conditions into a system of two second order equations by introducing an auxiliary variable v = !u and then apply an hp-mixed discontinuous Galerkin method to the resulting system. The unknown approximation vh of v can easily be eliminated to reduce the discrete problem to a Schur complement sys...

We study the evolution equation associated with biharmonic operator on infinite cylinders bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is asymptotic behaviour and positivity properties of solutions for large times. In particular, we derive local eventual solutions. furthermore prove heat its generalisations Euclidean space. main tools in our analysis are Four...

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

This report investigates the paper Lipman et al. Biharmonic distance, who introduced a new distance measure, called biharmonic. We examine the approach of the distance, which is based on the Green’s kernel of the Bi-Laplacian in the continuous and the discrete setting. For the discrete setting we have two different methods of calculation, an approximate as well as an exact computation. Furtherm...

We classify the space-like biharmonic surfaces in 3dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.

We deal with a weighted biharmonic problem in the unit ball of $\mathbb{R}^{4}$. The non-linearity is assumed to have critical exponential growth view Adam's type inequalities. weight $w(x)$ logarithm and potential $V$ positive continuous function on $\overline{B}$. It proved that there nontrivial weak solution this by mountain Pass Theorem. avoid loss compactness proving concentration result s...