Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : A stabilized mixed discontinuous Galerkin method for the incompressible miscible displacement problem | Luo et al. Boundary Value Problems 2011 2011 48 http content 2011 1 48 o Boundary Value Problems a SpringerOpen Journal RESEARCH Open Access A stabilized mixed discontinuous Galerkin method for the incompressible miscible displacement problem Yan Luo 1 Minfu Feng2 and Youcai Xu2 Correspondence xyc@ 2School of Mathematics Sichuan University Chengdu Sichuan 610064 Pr China Full list of author information is available at the end of the article Springer Abstract A new fully discrete stabilized discontinuous Galerkin method is proposed to solve the incompressible miscible displacement problem. For the pressure equation we develop a mixed stabilized discontinuous Galerkin formulation. We can obtain the optimal priori estimates for both concentration and pressure. Keywords Discontinuous Galerkin methods a priori error estimates incompressible miscible displacement 1 Introduction We consider the problem of miscible displacement which has considerable and practical importance in petroleum engineering. This problem can be considered as the result of advective-diffusive equation for concentrations and the Darcy flow equation. The more popular approach in application so far has been based on the mixed formulation. In a previous work Douglas and Roberts 1 presented a mixed finite element MFE method for the compressible miscible displacement problem. For the Darcy flow Masud and Hughes 2 introduced a stabilized finite element formulation in which an appropriately weighted residual of the Darcy law is added to the standard mixed formulation. Recently discontinuous Galerkin for miscible displacement has been investigated by numerical experiments and was reported to exhibit good numerical performance 3 4 . In Hughes-Masud-Wan 5 the method of 2 was extended to the discontinuous Galerkin framework for the Darcy flow. A family of mixed finite element discretizations of the Darcy flow equations using totally discontinuous elements was introduced
