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In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some interfaces. We show that the proposed scheme has optimal-order convergence rate unconditionally, without restriction on the grid ratio (between the time-step size and spatial mesh size). Previous works all required certain restrictions on the grid ratio except for the problem with globally smooth permeability and porosity. Our idea is to introduce an intermediate system of elliptic interface problems, whose solution is uniformly regular in each subdomain separated by the interfaces and its finite element solution coincides with the fully discrete solution of the original problem. In order to prove the boundedness of the fully discrete solution, we study the finite element discretization of the intermediate system of elliptic interface problems.
Fully discrete Galerkin finite element methods are studied for the equations of miscible displacement in porous media with the commonly-used Bear--Scheidegger diffusion-dispersion tensor: $$ D({bf u}) = gamma d_m I + |{bf u}|bigg( alpha_T I + (alpha_
We develop a theory for the problem of high pressure air injection into deep reservoirs containing light oil. Under these conditions, the injected fluid (oxygen + inert components) is completely miscible with the oil in the reservoir. Moreover, exoth
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this comp
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite element ap
We present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fing