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Volume 4, Issue 3, 1 December 2022, Pages 299-314
Abstract. We propose a penalty method to approximate the boundary condition of the Darcy system. For the penalty variational problem, we establish the well-posedness theorem and prove the optimal error estimates of the penalty in the continuous sense. Moreover, we apply the finite element method using RT0/P0 element to discretize the penalty variational problem. The convergence rate depending on both the penalty parameter and mesh size, as well as the applicability of the discrete scheme, are investigated through several numerical experiments on the cases with smooth/non-smooth and convex/non-convex domains.
How to Cite this Article:
G. Zhou, The penalty method for the boundary condition of the Darcy system, J. Appl. Numer. Optim. 4 (2022), 299-314.