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Local discontinuous Galerkin methods with explicit Runge‐Kutta time marching for nonlinear carburizing model
Author(s) -
Xia Chenghui,
Li Ying,
Wang Haijin
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4898
Subject(s) - carburizing , discontinuous galerkin method , runge–kutta methods , mathematics , nonlinear system , diffusion , galerkin method , constant (computer programming) , mathematical analysis , numerical analysis , finite element method , computer science , thermodynamics , materials science , physics , quantum mechanics , metallurgy , programming language
A fully discrete local discontinuous Galerkin (LDG) method coupled with 3 total variation diminishing Runge‐Kutta time‐marching schemes, for solving a nonlinear carburizing model, will be analyzed and implemented in this paper. On the basis of a suitable numerical flux setting in the LDG method, we obtain the optimal error estimate for the Runge‐Kutta–LDG schemes by energy analysis, under the condition τ ≤ λ h 2 , where h and τ are mesh size and time step, respectively, λ is a positive constant independent of h . Numerical experiments are presented to verify the accuracy and capability of the proposed schemes. For the carburizing diffusion processes of steel and the diffusion simulation for Cu‐Ni system, the numerical results show good agreement with the experimental results.