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A finite volume method for the Laplace equation on almost arbitrary two-dimensional grids

Komla Domelevo, Pascal Omnes (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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 Fortin operator for two-dimensional Taylor-Hood elements

Richard S. Falk (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

A free boundary problem for some modified predator-prey model in a higher dimensional environment

Hongmei Cheng, Qinhe Fang, Yang Xia (2022)

Applications of Mathematics

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 t goes to infinity and survives in the new environment, or it fails to establish...

A free boundary value problem in potential theory

Guido Stampacchia, D. Kinderlehrer (1975)

Annales de l'institut Fourier

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 Ω and a function u defined in Ω satisfying the given differential equation together with both Dirichlet and Neumann type data on the boundary of Ω . 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 method for semilinear elliptic equation

Fei Xu, Hehu Xie (2017)

Applications of Mathematics

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...

A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

Jean-Paul Daniel (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A general perturbation formula for electromagnetic fields in presence of low volume scatterers

Roland Griesmaier (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

Yves Capdeboscq, Michael S. Vogelius (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

A general representation formula for boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction

Yves Capdeboscq, Michael S. Vogelius (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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 5491