Analysis of backward Euler/Spectral discretization for an evolutionary mass and heat transfer in porous medium
Provides rigorous numerical analysis for a specific coupled PDE system in porous media flow, but the results are incremental and domain-specific.
The authors prove existence, uniqueness, and optimal a priori error estimates for a spectral discretization of coupled Darcy and reaction-diffusion equations modeling mass and heat transfer in porous media, with numerical tests confirming the theory.
This paper presents the unsteady Darcy's equations coupled with two nonlinear reaction-diffusion equations, namely this system describes the mass concentration and heat transfer in porous media. The existence and uniqueness of the solution are established for both the variational formulation problem and for its discrete one obtained using spectral discretization. Optimal a priori estimates are given using the Brezzi-Rappaz-Raviart theorem. We conclude by some numerical tests which are in agreement with our theoretical results.