| Abstract: |
| We consider a coupled micro-macro parabolic-elliptic system of partial differential equations (PDEs) modelling the interplay between two pressures in a gas-liquid mixture close to equilibrium that is filling a porous
medium with distributed microstructures. We prove well-posedness for the space-discrete time-continuous problem using a semidiscrete Galerkin scheme.
We obtain a priori error estimates and convergence rates for the discretized problem. Additionally, we design an a-priori feedback strategy that refines the mesh in a pre-computational stage to reduce the overall numerical error. |
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