Sharp Expressions for the Stabilization Parameters in Symmetric Interior-penalty Discontinuous Galerkin Finite Element Approximations of Fourth-order Elliptic Problems

Abstract

Abstract In this paper, we derive explicit expressions for the penalty parameters appearing in symmetric and semi-symmetric interior-penalty discontinuous Galerkin finite element method (DGFEM) for fourth-order elliptic problems. We demonstrate the sharpness of the theoretically predicted penalty parameter values through numerical experiments.