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Characteristic splitting mixed finite element analysis of compressible wormhole propagation. (English) Zbl 1435.65169

The authors discuss a combined method for simulating the compressible wormhole propagation that relies on the splitting mixed finite element. This leads to a separated symmetric positive definite mixed element system which avoids the solvability of a large-scale coupled system. Optimal error estimates in the \(L^2\)-norm are derived for pressure, velocity, concentration and porosity. Numerical experiments are included to support the theoretial findings.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76N15 Gas dynamics (general theory)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76R50 Diffusion
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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