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Displaying 101 –
120 of
5493
We present a finite volume method based on the integration of the Laplace
equation on both the cells of a primal almost arbitrary two-dimensional
mesh and those of a
dual mesh obtained by joining the centers of the cells of the primal mesh.
The key ingredient is the definition of discrete gradient and divergence
operators verifying a discrete Green formula.
This method generalizes an existing finite volume method that
requires “Voronoi-type” meshes.
We show the equivalence of this finite volume...
A standard method for proving the inf-sup condition implying stability of
finite element approximations for the stationary Stokes equations is to
construct a Fortin operator. In this paper, we show how this can be done
for two-dimensional triangular and rectangular Taylor-Hood methods, which
use continuous piecewise polynomial approximations for both velocity and
pressure.
We focus on the free boundary problems for a Leslie-Gower predator-prey model with radial symmetry in a higher dimensional environment that is initially well populated by the prey. This free boundary problem is used to describe the spreading of a new introduced predator. We first establish that a spreading-vanishing dichotomy holds for this model. Namely, the predator either successfully spreads to the entire space as goes to infinity and survives in the new environment, or it fails to establish...
This paper is devoted to the formulation and solution of a free boundary problem for the Poisson equation in the plane. The object is to seek a domain and a function defined in satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of . The Neumann data are given in a manner which permits reformulation of the problem as a variational inequality. Under suitable hypotheses about the given data, it is shown that there exists a unique solution...
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and semilinear problems on a very low dimensional space. The linearized boundary value problems are solved by some multigrid iterations. Besides the multigrid iteration, all other efficient numerical methods can also serve as...
We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter ε which extend those proposed by Kohn and Serfaty [21]. These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution...
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields.
This...
In several practically interesting applications of electromagnetic scattering theory like, e.g., scattering from small point-like objects such as buried artifacts or small inclusions in non-destructive testing, scattering from thin curve-like objects such as wires or tubes, or scattering from thin sheet-like objects such as cracks, the volume of the scatterers is small relative to the volume of the surrounding medium and with respect to the wave length of the applied electromagnetic fields.
This...
We establish an asymptotic representation formula for the steady state voltage perturbations caused by low volume fraction internal conductivity inhomogeneities. This formula generalizes and unifies earlier formulas derived for special geometries and distributions of inhomogeneities.
We establish an asymptotic representation formula for the steady state voltage
perturbations caused by low volume fraction internal conductivity
inhomogeneities. This formula generalizes and unifies earlier
formulas derived for special geometries and distributions
of inhomogeneities.
Currently displaying 101 –
120 of
5493