Legendre-based model order reduction method for solving convection–diffusion equations with variable coefficients

A model order reduction method based on shifted Legendre polynomials for solving convection–diffusion equations with variable coefficients is presented in this paper. The ordinary differential system of the convection–diffusion equation is obtained by finite element discretization procedure. Then, approximating the system state via shifted Legendre polynomials, the reduced-order system is produced, which can be solved efficiently to obtain the numerical solution. Error analysis is presented, and numerical examples are used to verify the feasibility of the presented method.