  In this paper we present and analyze a constraint energy minimizing
generalized multiscale finite element method for convection diffusion equation.
To define the multiscale basis functions, we first build an auxiliary
multiscale space by solving local spectral problems motivated by analysis. Then
constraint energy minimization performed in oversampling domains is exploited
to construct the multiscale space. The resulting multiscale basis functions
have a good decay property even for high contrast diffusion and convection
coefficients. Furthermore, if the number of oversampling layer is chosen
properly, we can prove that the convergence rate is proportional to the coarse
mesh size. Our analysis also indicates that the size of the oversampling domain
weakly depends on the contrast of the heterogeneous coefficients. Several
numerical experiments are presented illustrating the performances of our
method.
