Abstract
Partial differential equations are an important part of mathematics in science and its numerical solution occupies an important position in the numerical analysis. Partial differential equations are closely related to human life and it has important research value. At present, people have studied its solutions in depths and achieved a lot of valuable results. The current solution is the finite element method and finite different method. The convection-diffusion equation is more closely related to human activities, especially complex physical processes. The behavior of many parameters in flow phenomena follows the convection-diffusion equation, such as momentum and heat. The convection-diffusion equation is also used to describe the diffusion process in environmental science, such as the pollutant transport in the atmosphere, oceans, lakes, rivers or groundwater. The research of the convection-diffusion equation is of great importance. Partial differential equation theory has important applications in the solution of the convection-diffusion equation. This chapter mainly talks about the application of the finite difference method in the solution of the convection-diffusion equation.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Liu, J.: Ill-posed problems of regularization and application, vol. 3(2), pp. 12–19. Science Press, Beijing (2005)
Xiao, T., Yu, S., Wang, Y.: Numerical solution of inverse problems, vol. 4(5), pp. 78–80. Science Press, Beijing (2003)
Burden, R.L.: Numerical Analysis, 7th edn., vol. 8(3), pp. 11–19. Higher education press (2001)
Bjorck, A.: Least Squares Methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. 1(3), pp. 90–99 (1990)
Ting, L., Cheng, J.: Numerical methods, vol. 7(11), pp. 110–117. Beijing University of Technology Press, Beijing (2005)
Song, X.W.: Order elliptic partial differential operators from over specified boundary data, in “Improperly posed problems”. Pitman san Francisco 7(2), 23–31 (1977)
Bands, H.T., Kunisch, K.: An approximation theory for nonlinear differential equation with application to identification and control. SIAM, J. Control Optimal. 20(3), 815–849 (1982)
Haberman, R.: Applied Partial Differential Equations, vol. 3(6), pp. 10–20. Mechanical industry press (2007)
Qiu, J.-M., Shu, C.-W.: Convergence of High Order Finite Volume Weighted Essentially Nonoscillatory Scheme and Discontinuous Galerkin Method for Nonconvex Conservation Laws. SIAM Journal on Scientific Computing 31(1), 584–607 (2008)
Persson, P.-O., Peraire, J.: Newton-GMRES Preconditioning for Discontinuous Galerkin Discretizations of the Navier–Stokes Equations. SIAM Journal on Scientific Computing 30 30(6), 2709–2733 (2008)
Warburton, T., Hagstrom, T.: Taming the CFL Number for Discontinuous Galerkin Methods on Structured Meshes. SIAM Journal on Numerical Analysis 46(6), 3151–3180 (2008)
Pietro, D.A.D., Ern, A., Guermond, J.-L.: Discontinuous Galerkin Methods for Anisotropic Semidefinite Diffusion with Advection. SIAM Journal on Numerical Analysis 46(2), 805–831 (2008)
Vergara, C., Zunino, P.: Multiscale Boundary Conditions for Drug Release from Cardiovascular Stents. Multiscale Modeling & Simulation 7(2), 565–588 (2008)
Peraire, J., Persson, P.-O.: The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems. SIAM Journal on Scientific Computing 30(4), 1806–1824 (2008)
Girault, V., Sun, S., Wheeler, M.F., Yotov, I.: Coupling Discontinuous Galerkin and Mixed Finite Element Discretizations using Mortar Finite Elements. SIAM Journal on Numerical Analysis 46(2), 949–979 (2008)
Ern, A., Guermond, J.-L.: Discontinuous Galerkin Methods for Friedrichs’ Systems. Part III. Multifield Theories with Partial Coercivity. SIAM Journal on Numerical Analysis 46(2), 776–804 (2008)
Wang, W., Li, X., Shu, C.-W.: The Discontinuous Galerkin Method for the Multiscale Modeling of Dynamics of Crystalline Solids. Multiscale Modeling & Simulation 7(1), 294–320 (2008)
Xu, Y., Shu, C.-W.: A Local Discontinuous Galerkin Method for the Camassa–Holm Equation. SIAM Journal on Numerical Analysis 46(4), 1998–2021 (2008)
Ern, A., Guermond, J.L.: Discontinuous Galerkin Methods for Friedrichs’ Systems. Part II. Second order Elliptic PDEs. SIAM Journal on Numerical Analysis 44(6), 2363–2388 (2006)
Kamga, J.B.A., Després, B.: CFL Condition and Boundary Conditions for DGM Approximation of Convection Diffusion. SIAM Journal on Numerical Analysis 44(6), 2245–2269 (2006)
Ye, X.: A Discontinuous Finite Volume Method for the Stokes Problems. SIAM Journal on Numerical Analysis 44(1), 183–198 (2006)
Buffa, A., Perugia, I.: Discontinuous Galerkin Approximation of the Maxwell Eigenproblem. SIAM Journal on Numerical Analysis 44(5), 2198–2226 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Peng, Y., Liu, C., Shi, L. (2013). Soution of Convection-Diffusion Equations. In: Yang, Y., Ma, M., Liu, B. (eds) Information Computing and Applications. ICICA 2013. Communications in Computer and Information Science, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53703-5_56
Download citation
DOI: https://doi.org/10.1007/978-3-642-53703-5_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53702-8
Online ISBN: 978-3-642-53703-5
eBook Packages: Computer ScienceComputer Science (R0)