High Order Numerical Solutions to Convection Diffusion Equations withDifferent Approaches

[摘要] Convection diffusion equations, one of the fundamental kinds of nonlinear partial differential equations (PDE),describe a variety of phenomena such as fluid convection and diffusion and traffic flow etc. This paper uses fourdifferent approaches to handle nonlinearity in convection diffusion equations. High order accuracy numerical solutionsto nonlinear PDE were acquired with several discretization methods: spectral modal and nodal element, finiteelement, and compact difference methods. Numerical results were compared with exact solutions to demonstrate theerror convergence rate. For irregular domains where exact solutions are unavailable, very high accuracy numericalsolutions were used for error comparisons. Pros and cons of these four approaches for handling nonlinearity werereviewed and discussed. This study provides a reference in solving nonlinear PDE with different options.

[关键词] Spectral element method;Finite element method;Compact difference method;Convection diffusion equation;Lagrangeinterpolation