May 11 – Sarah Ali Hassan: A posteriori error estimates and stopping criteria for solvers using domain decomposition methods and with local time stepping

Sarah Ali Hassan: Thursday 11 May at 3 pm, A415 Inria Paris.
In this work we develop a posteriori error estimates and stopping criteria for domain decomposition (DD) methods with optimized Robin transmission conditions on the interface. Steady diffusion equation using the mixed finite element (MFE) discretization as well as in the heat equation using the MFE method in space and the discontinuous Galerkin scheme in time are analysed. For the heat equation, a global-in-time domain decomposition method is used, allowing for different time steps in different subdomains. We bound the error between the exact solution of the PDE and the approximate numerical solution at each iteration of the domain decomposition algorithm. Different error components (domain decomposition, space discretization, time discretization) are distinguished, which allows us to define efficient stopping criteria for the DD algorithm. The estimates are based on the reconstruction techniques for pressures and fluxes. Numerical experiments illustrate the theoretical findings.

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