# Article

**Keywords:**

multilevel correction; adaptive finite element method; Steklov eigenvalue problem; numerical experiment

**Summary:**

Adaptive finite element method based on multilevel correction scheme is proposed to solve Steklov eigenvalue problems. In this method, each adaptive step involves solving associated boundary value problems on the adaptive partitions and small scale eigenvalue problems on the coarsest partitions. Solving eigenvalue problem in the finest partition is not required. Hence the efficiency of solving Steklov eigenvalue problems can be improved to the similar efficiency of the adaptive finite element method for the associated boundary value problems. The efficiency of the proposed method is also investigated by a numerical experiment.