A multigrid discretization scheme for the Steklov eigenproblem

In this paper, we discusses the finite element approximation for a Steklov eigenvalue problem. Based on the work of Armentano and Padra, we derive an a posteriori error estimate. By constructing auxiliary bubble functions and lifting operators, we prove the reliability and validity of the posterior error estimator. In addition, we verify the robustness of the posterior error estimator under the adaptive grid through numerical experiments.