A multiscale method for a Convection-Diffusion equation
Aboubacar Konaté · HAL (Le Centre pour la Communication Scientifique Directe) · 2018
In this work, we introduce a new multiscale method based on discontinuous Galerkin (dG) discretization for solving a dominated convection equation with parameters varying at a very small space scale. This is motivated by the fact that in some applications (for example in transport flow), particulary when the parameters are discontinuous or when the geometry is complex (non-conformities, faults, ...), dG discretizations are more suitable than those based on finite volume or continuous finite elements. Moreover, the use of a dG method allows to treat easily the convection term by upwinding. Using standard methods when the parameters are varying at a very small space scale is demanding in term of computing times and in term of computer memory. Roughly speaking, multiscale methods consist in building basis functions which take into account the variation of parameters which leads to better balance between accuracy and computing times. An error estimate is established where the parameters are assumed to be periodic. Numerical illustrations are presented.