Abstract
This paper concerns the energy deposition of high-energy(e.g., $\approx 50-500$ MeV) proton and carbon ions andhigh-energy electrons (of $\approx 50$ MeV), in inhomogeneous media. Our goal is to develop a flexiblemodel incorporated with the analytic theory for ions based on bipartition and Fokker-Planck developments. Both procedures areleading to convection dominated convection diffusion equations.We study convergence for semi-discreteand fully discreteapproximations of a such obtained equation, for abroad beam model, using the standard Galerkinand streamline diffusion finite element methods.The analytic broad beam model of the light ion absorbed dose were comparedwith the results of the modified Monte Carlo (MC) code SHIELD-HIT+ andthose of Galerkin streamline diffusion approach.
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