A Priori Error Estimates and Computational Studies for a Fermi Pencil-Beam Equation
Journal article, 2018

We derive a priori error estimates for the standard Galerkin and streamline diffusion finite element methods for the Fermi pencil-beam equation obtained from a fully three-dimensional Fokker-Planck equation in space and velocity variables. For a constant transport cross-section, there is a closed form analytic solution available for the Fermi equation with a data as product of Dirac functions. Our objective is to study the case of nonconstant, nonincreasing transport cross-section. Therefore we start with a theoretical, that is, a priori, error analysis for a Fermi model with modified initial data in L-2. Then we construct semi-streamline-diffusion and characteristic streamline-diffusion schemes and consider an adaptive algorithm for local mesh refinements. To derive the stability estimates, for simplicity, we rely on the assumption of nonincreasing transport cross-section. Different numerical examples, in two space dimensions are justifying the theoretical results. Implementations show significant reduction of the computational error by using such adaptive procedure.

reliability

a priori error estimates

duality argument

Fermi and Fokker-Planck pencil-beam equations

efficiency

adaptive finite element method

Author

M. Asadzadeh

University of Gothenburg

Larisa Beilina

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Muhammad Naseer

Student at Chalmers

Christoffer Standar

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Journal of Computational and Theoretical Transport

2332-4309 (ISSN) 2332-4325 (eISSN)

Vol. 47 1-3 125-151

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1080/23324309.2018.1496937

More information

Latest update

10/23/2019