Big Natterporn Cheurnjaren
Title: Conservative local discontinuous Galerkin method for compressible miscible displacements in porous media
Nonconservative local discontinuous Galerkin (LDG) method for both
flow and transport equations was introduced for the one-dimensional coupled system
of compressible miscible displacement problem. In this paper, we will continue our
effort and develop a conservative LDG method for the problem in two space dimensions.
Optimal error estimates in \[L^\infty(0, T ;L2)\] norm for not only the solution itself but also the
auxiliary variables will be derived. The main difficulty is how to treat the inter-element
discontinuities of two independent solution variables (one from the flow equation and
the other from the transport equation) at cell interfaces. Numerical experiments will be
given to confirm the accuracy and efficiency of the scheme.