Nonoverlapping discretization methods for partial differential equations

Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse‐mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector‐space‐framework. Using it, it is possible to develop algorithms that satisfy the DDM‐paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 1427–1454, 2014