A Priori Error Estimates and Computational Studies for a Fermi Pencil-Beam Equation
Artikel i vetenskaplig tidskrift, 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.


adaptive finite element method

Fermi and Fokker-Planck pencil-beam equations


duality argument

a priori error estimates


M. Asadzadeh

Göteborgs universitet

Larisa Beilina

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Muhammad Naseer

Student vid Chalmers

Christoffer Standar

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Journal of Computational and Theoretical Transport

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

Vol. 47 1-3 125-151



Sannolikhetsteori och statistik

Matematisk analys



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