A posteriori error analysis for Schwarz overlapping domain decomposition methods

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis both multiplicative and additive overlapping Schwarz domain methods. The in user-specified functional (quantity interest) is decomposed into contributions that arise as result finite iteration between subdomains from spatial discretization. discretization contribution further arising each subdomain. This to construct two stage strategy efficiently reduces quantity interest by adjusting relative error.