Abstract
In this work, the penalty method is studied for the mixed Stokes-Darcy problem, motivated by the penalty method applied to Stokes equation. This work first proposes the penalty Stokes-Darcy model at the continuous level. Then we prove that the solution of the penalty model converges strongly to the original solution as Oϵ in which the penalty parameter is ϵ→0. What’s more, the finite element method is used to solve the penalty model and the optimal error estimates are presented. Finally, several numerical tests are carried out to verify our theoretical results.
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