| Abstract: | Two-grid finite element methods for the steady Navier-Stokes/Darcy modelare considered. Stability and optimal error estimates in the $H^1$-norm for velocity andpiezometric approximations and the $L^2$-norm for pressure are established under meshsizes satisfying $h=H^2$. A modified decoupled and linearised two-grid algorithm isdeveloped, together with some associated optimal error estimates. Our method andresults extend and improve an earlier investigation, and some numerical computationsillustrate the efficiency and effectiveness of the new algorithm. |
