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

TL;DR

This paper introduces two-grid and local finite element schemes for a challenging non-selfadjoint Stekloff eigenvalue problem, providing error analysis and numerical validation of their efficiency.

Contribution

It develops and analyzes new two-grid and local finite element discretization schemes for a non-selfadjoint, non-H^1-elliptic Stekloff eigenvalue problem, including error estimates.

Findings

Error estimates for two-grid discretizations

Effective local error estimate near boundary singularities

Numerical experiments confirm scheme efficiency

Abstract

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