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A posteriori error estimates for the generalized Schwarz method of a new class of advection‐diffusion equation with mixed boundary condition

In this paper, a posteriori error estimates for the generalized Schwarz method with mixed boundary condition on the interfaces for advection‐diffusion equation with second‐order boundary value problems are proved using theta time scheme combined with Galerkin spatial method. Furthermore, a asymptotic behavior in Sobolev norm is deduced using Benssoussan‐Lions' algorithm.