Mesh independence of the condition number of discrete galerkin systems by preconditioning

Abstract

In the paper [1] the author proves that preconditioning the discrete Galerkin system by the Choleski factors of the Gramian we obtain a mesh independent condition number. In the present paper we generalize this method by using the Choleski factors of a term from a special splitting of the Gramian. Thus, we obtain the method from [1] like a particular case. We also observe that such a kind of splitting can be obtained by an incomplete Choleski decomposition of the Gramian.