Abstract. In this paper we present the first results on substructuring methods for nonlocal operators, specifically, an instance of the nonlocal p-Laplace operator. We present a nonlocal variational formulation of this operator, proving a nonlocal Poincaré inequality and upper bound to establish a spectral equivalence. We then introduce a nonlocal two-domain variational formulation utilizing no...

We describe a non-overlapping domain decomposition algorithm for nonlinear porous media flows discretized with the multiscale mortar mixed finite element method. There are two main ideas: (1) linearize the global system in both subdomain and interface variables simultaneously to yield a single Newton iteration; and (2) algebraically eliminate subdomain velocities (and optionally, subdomain pres...

The goal of this paper is to develop the theory Schur complementation in context operators acting on anti-dual pairs. As a byproduct, we obtain natural generalization parallel sum and difference, as well Lebesgue-type decomposition. To demonstrate how operator approach works application, derive corresponding results for rigged Hilbert spaces, representable functionals ⁎-algebras.

Several representations of the generalized Drazin inverse of a block matrix with a group invertible generalized Schur complement in Banach algebra are presented.