A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system. (English) Zbl 07490872
Summary: In this article, we consider the time-dependent convection-diffusion-reaction equation coupled with the Darcy equation. We propose a numerical scheme based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. We establish optimal a posteriori error estimates with two types of computable error indicators, the first one linked to the time discretization and the second one to the space discretization. Finally, numerical investigations are performed and presented.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 76-XX | Fluid mechanics |
Keywords:
Darcy’s equations; convection-diffusion-reaction equation; finite element method; a posteriori error estimates; adaptive methodsSoftware:
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