Conforming and non-conforming virtual element methods for the biharmonic Steklov eigenvalue problem with minimum regularity (opens in new tab)

In this work, we analyze the conforming and $C^0$-non-conforming Virtual Element Method for a fourth-order Steklov eigenvalue problem on a generally shaped, possibly nonconvex, polygonal domain. By employing an {\it enriching } operator, we derive the convergence analysis using the discrete $H^2$ seminorm, and the $H^1$ and $L^2$ norms. We use the Babu\v{s}ka--Osborn spectral theory \cite{BO} to prove that the numerical scheme approximates the s...