An improvement of the theorem of a posteriori estimates for inverse elliptic operators

Abstract

This paper presents a numerical method to verify the invertibility of a linear elliptic operator. The invertibility of a linearized operator is useful information when verifying the existence of a solution for the corresponding nonlinear elliptic partial differential equations (PDEs). The proposed method is proved on the function spaces more suitable than previous methods. The a posteriori estimate, which is expected to converge to the exact operator norm of the inverse elliptic operators, is obtained by less computational cost than existing methods.