Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index
نویسندگان
چکیده
منابع مشابه
Finite element approximation of the Sobolev constant
Denoting by S the sharp constant in the Sobolev inequality in W 0 (B), being B the unit ball in R, and denoting by Sh its approximation in a suitable finite element space, we show that Sh converges to S as h ↘ 0 with a polynomial rate of convergence. We provide both an upper and a lower bound on the rate of convergence, and present some numerical results.
متن کاملDerivation of the Radiative Transfer Equation Inside a Moving Semi-Transparent Medium of Non Unit Refractive Index
The derivation of the radiative transfer equation inside a moving semi-transparent medium of non unit constant refractive index has been completely achieved, leading to an exactly similar equation as in the case of a unit index, unless it is expressed in a particular frame with particular time and space co-ordinates; defining first the “equivalent vacuum” and the “matter” space associated to it...
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملThe Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation
A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...
متن کاملFinite Element Approximation of the Cahn-Hilliard-Cook Equation
We study the nonlinear stochastic Cahn-Hilliard equation driven by additive colored noise. We show almost sure existence and regularity of solutions. We introduce spatial approximation by a standard finite element method and prove error estimates of optimal order on sets of probability arbitrarily close to 1. We also prove strong convergence without known rate.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 2015
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2014.11.025