Some remarks on the rigorous estimation of inverse linear elliptic operators

Abstract

This paper presents a new numerical method to obtain the rigorous upper bounds of inverse linear elliptic operators. The invertibility of a linearized operator and its norm estimates give important informations when analyzing the nonlinear elliptic partial differential equations (PDEs). The computational costs depend on the concerned elliptic problems as well as the approximation properties of used finite element subspaces, e.g., mesh size or so. We show the proposed new estimate is effective for an intermediate mesh size.