s of IWANASP, October 22 – 24, 2015, Lagos, Portugal A FAST FOURIER–GALERKIN METHOD SOLVING A BOUNDARY INTEGRAL EQUATION FOR THE BIHARMONIC EQUATION

In this paper we review fourth-order approximations of the biharmonic operator in one, two and three dimensions. In addition, we describe recent developments on second and fourth order finite difference approximations of the two dimensional Navier-Stokes equations. The schemes are compact both for the biharmonic and the Laplacian operators. For the convective term the fourth order scheme invoke...

where τ( f ) is the tension field of f and dvg is the volume form of M. It is clear that E2( f |Ω) = 0 on any compact domain if and only if f is a harmonic map. Thus E2 provides a measure for the extent to which f fails to be harmonic. If f is a critical point of (1.1) over every compact domain, then f is called a biharmonic map or 2-harmonic maps. Jiang [10] proved that f is biharmonic if and ...

This paper is concerned with the stability of inverse source problem for damped biharmonic plate equation in three dimensions. The estimate consists Lipschitz type data discrepancy and high frequency tail function, where latter decreases as upper bound increases. also shows exponential dependence on damping coefficient. ingredients analysis include Carleman estimates time decay wave to obtain a...

We present the problem of tracing rays in 2D and 3D heterogeneous isotropic media as a set of optimization problems. Each optimization problem is obtained by applying Fermat's principle to an approximation of the travel time equation from a xed source to a xed receiver. We assume a piecewise linear raypath which simpliies the computations of the problem, in the same way Mao and Stuart suggested...

In this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of Kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎Using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

In this work, the least squares weighted residual method is used to solve the two-dimensional (2D) elasticity problem of a rectangular plate of in-plane dimensions 2a 2b subjected to parabolic edge tensile loads applied at the two edges x = a. The problem is expressed using Beltrami–Michell stress formulation. Airy’s stress function method is applied to the stress compatibility equation, and th...