| The numerical solution of compressible miscible displacement was trea-ted by Douglas and Roberts in "Numerical methods for a model for com-pressible miscible displacement in porous media". In the same year, incom-pressible miscible displacement was proposed and analyzed in a periodic setting by Douglas,J.Jr.,Ewing,R.E.,Wheeler and M.F. in "The approxi-mation of the pressure by a mixed method in the simulation of miscible displacement". Several recent works have been devoted to the superconver-gence of the Darcy velocity along Gauss lines for the mixed finite element method. And Ewing et al. pointed out that it is natural to combine the mixed method for the pressure with the standard finite element method for the concentration.An application of superconvergence was proposed and analyzed by Chen Yan-ping.In order to retain the superconvergence estimates of Ew-ing ct al,an extension of the Darcy velocity was used. In the concentration equation, the Darcy velocity u was placed by u*. And the terms includ-ing u*were treated with the conclusions and lemmas about u*which were obtained by Ewing et al.(?) was treated by L2projection.A nonlinear parabolic system describing compressible nuclear waste disposal contamination in porous media is presented. This system includes four equations:the Fluid equation, the Heat equation, the Brine equation and the Radionuclide equation. These equations were treated with Chen Yan-ping’s method, using u*. When the Heat equation was treated, an extension of the pressure was used,also. Considering these four equations are coupled equations,they should be treated in appropriate order.In this paper, the semi-discrete schemes and the full-discrete schemes of the mixed finite-clement and the standard finite-element approximation arc established for compressible flow of contamination from nuclear waste in porous media, and the errors are analyzed. At last, the superconver- gencc results of the semi-discrete schemes and the full-discrete schemes arc obtained. |
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