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This work aims to extend the residual distribution (RD) framework to stiffrelaxation problems. The RD is a class of schemes which is used to solvehyperbolic system of partial differential equations. Up to our knowledge, itwas used only for systems with mild source terms, such as gravitation problemsor shallow water equations. What we propose is an IMEX (implicit--explicit)version of the residual distribution schemes, that can resolve stiff sourceterms, without refining the discretization up to the stiffness scale. This canbe particularly useful in various models, where the stiffness is given bytopological or physical quantities, e.g. multiphase flows, kinetic models,viscoelasticity problems. Moreover, the provided scheme is able to catchdifferent relaxation scales automatically, without losing accuracy. The schemeis asymptotic preserving and this guarantees that in the relaxation limit, werecast the expected macroscopic behaviour. To get a high order accuracy, we usean IMEX time discretization combined with a Deferred Correction (DeC)procedure, while naturally RD provides high order space discretization.Finally, we show some numerical tests in 1D and 2D for stiff systems ofequations.

Asymptotic preserving Deferred Correction Residual Distribution schemes