Based on the heterogeneous multiscale method, this paper presents a finite volume method to solve multiscale convection-diffusion-reaction problem. The paper constructs an algorithm of the optimal order convergence rate in H1-norm under periodic medias.
AbstractThis paper presents a convergence analysis for the exponentially fitted finite volume method in two dimensions applied
to a linear singularly perturbed convection-diffusion equation with exponential boundary layers. The method is formulated
as a nonconforming Petrov-Galerkin finite element method with an exponentially fitted trial space and a piecewise constant
test space. The corresponding bilinear form is proved to be coercive with respect to a discrete energy norm. Numerical results are presented to
verify the theoretical rates of convergence.
Error Estimates for the Heterogeneous Multiscale Finite Volume Method of Convection-Diffusion-Reaction Problem