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Local discontinuous Galerkin method for solving an N ‐carrier system
Author(s) -
Zhang Rongpei,
Yu Xijun,
Zhao Guozhong
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21694
Subject(s) - discontinuous galerkin method , mathematics , norm (philosophy) , galerkin method , boundary value problem , partial differential equation , stability (learning theory) , partial derivative , mathematical analysis , finite element method , computer science , physics , thermodynamics , machine learning , political science , law
In this article, we present local discontinuous Galerkin (LDG) method for solving a model of energy exchanges in an N ‐carrier system with Neumann boundary conditions. This model extends the concept of the well‐known parabolic two‐step model for microheat transfer to the energy exchanges in a generalized N ‐carrier system with heat sources. The energy norm stability and error estimate of the LDG method is proved for solving N ‐carrier system. Some numerical examples are given. The numerical results when compared with the exact solution and other numerical results indicate that the present method is seen to be a very good alternative to some existing techniques for realistic problems. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011