A posteriori error estimate for the non-stationary concentration equation coupled with the Darcy system discretized by the Raviart–Thomas finite element
摘要
This article focuses on discretizing the convection–diffusion–reaction equation (concentration or heat), which is time-dependent and coupled with the Darcy equation. The Darcy system is discretized using the Raviart–Thomas finite element, while the concentration equation is discretized using the Lagrange finite element of order one in space and the Euler method in time. We present optimal a posteriori error estimates utilizing two computable error indicators: linearization and discretization indicators. Ultimately, numerical experiments demonstrate and confirm the efficacy of the proposed method, and show comparisons with previous works.