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This paper studies and analyzes a model describing the flow of contaminated brines through the porous media under severe thermal conditions caused by the radioactive contaminants. The problem is approximated based on combining the mixed finite element method with the modified method of characteristics. In order to solve the resulting algebraic nonlinear equations efficiently, a two-grid method is presented and discussed in this paper. This approach includes a small nonlinear system on a coarse grid with size  H and a linear system on a fine grid with size  h . It follows from error estimates that asymptotically optimal accuracy can be obtained as long as the mesh sizes satisfy  H = O h 1 / 3 .

A Numerical Method for Compressible Model of Contamination from Nuclear Waste in Porous Media