Results 221 to 230 of about 51,079 (267)

Zero extension for Poisson’s equation

Science China Mathematics, 2019
The paper under review deals with a necessary and sufficient condition to ensure that the extension by zero of the solution of the (homogeneous) Dirichlet problem for the Poisson equation with right hand side \(f\) solves the (homogeneous) Dirichlet problem for the Poisson equation with the extension by zero of \(f\) as right hand side.
Cai, Yongyong, Zhou, Shulin
openaire   +1 more source

Collocation methods for Poisson’s equation

Computer Methods in Applied Mechanics and Engineering, 2006
The main feature of the present paper is that the collocation method is treated as the least squares method involving integration approximation. Dirichlet, Neumann and Robin boundary value problems are considered. Based on integration approximation, the authors locate not only the collocation nodes, but they are also concerned with the error analysis ...
Hu, Hsin-Yun, Li, Zi-Cai
openaire   +2 more sources

QUASICONFORMAL SOLUTIONS OF POISSON EQUATIONS

Bulletin of the Australian Mathematical Society, 2015
The main aim of this paper is to establish the Lipschitz continuity of the $(K,K^{\prime })$-quasiconformal solutions of the Poisson equation ${\rm\Delta}w=g$ in the unit disk $\mathbb{D}$.
Li, Peijin, Chen, Jiaolong, Wang, Xiantao   +2 more
openaire   +2 more sources

The Poisson Equation

2005
AbstractThis chapter concerns the statement of the Poisson equation and its weak formulation. This is followed by a description of finite element discretization and properties of the discrete problem.
Howard C Elman, David J Silvester, Andrew J Wathen   +2 more
openaire   +1 more source

Poisson’s Equation

1974
We begin with some Lemmas regarding the smoothness of the potential of a measure on the support of the measure.
openaire   +1 more source

CUBATURE SOLUTION OF THE POISSON EQUATION

Communications in Numerical Methods in Engineering, 1997
The solutions of the Poisson equation in regular and irregular shaped physical domains are obtained by the cubature method. The solutions of the three test problems involving regular shaped domains are compared with the analytical solutions and the control-volume, five-point finite difference, Galerkin finite element and quadrature numerical solutions.
Escobar, Freddy H., Jongkittinarukorn, Kittiphong, Civan, Faruk   +2 more
openaire   +2 more sources

Poisson’s equation

2000
Poisson’s equation is the inhomogeneous equivalent of Laplace’s equation. It is encountered in the modelling of a variety of problems in mechanics and physics, ranging from the study of fluid flows in porous media to the theory of gravitation, In Chapter 5 dealing with Laplace’s equation, we have briefly encountered Poisson’s equation in connection ...
openaire   +1 more source

Analogy in Solving Poisson's Equation

Canadian Mathematical Bulletin, 1975
The passage from ordinary to partial differential equations is a difficult one. While many properties of ordinary differential equations admit analogies in the framework of partial differential equations, the techniques used to establish them may bear little resemblance to those which suffice in the simpler setting.
openaire   +1 more source

On the Equation of Euler–Poisson–Darboux

SIAM Journal on Mathematical Analysis, 1973
Weak solutions of the initial value problem for the EPD equation are constructed using distributional methods. After taking the Fourier transform with respect to the space variables we obtain an equation related to the Bessel differential equation which can easily be solved.
openaire   +2 more sources

THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY

Journal of Hyperbolic Differential Equations, 2008
In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation.
Jin, Shi, Liao, Xiaomei, Yang, Xu
openaire   +2 more sources