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In this paper, for a new Stekloff eigenvalue problem which is non-selfadjointand not $H^1$-elliptic, we establish and analyze two kinds of two-griddiscretization scheme and a local finite element scheme. We present the errorestimates of approximations of two-grid discretizations. We also prove a localerror estimate which is suitable for the case that the local refined regioncontains singular points lying on the boundary of domain. Numerical experimentsare reported finally to show the efficiency of our schemes.

Two-grid discretizations and a local finite element scheme for a non-selfadjoint Stekloff eigenvalue problem