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In [1] is proposed a simplified DeC method, that, when combined with theresidual distribution (RD) framework, allows to construct a high order,explicit FE scheme with continuous approximation avoiding the inversion of themass matrix for hyperbolic problems. In this paper, we close some open gaps inthe context of deferred correction (DeC) and their application within the RDframework. First, we demonstrate the connection between the DeC schemes and theRK methods. With this knowledge, DeC can be rewritten as a convex combinationof explicit Euler steps, showing the connection to the strong stabilitypreserving (SSP) framework. Then, we can apply the relaxation approachintroduced in [2] and construct entropy conservative/dissipative DeC (RDeC)methods, using the entropy correction function proposed in [3].  [1] R. Abgrall. High order schemes for hyperbolic problems using globallycontinuous approximation and avoiding mass matrices. Journal of ScientificComputing, 73(2):461--494, Dec 2017.  [2] D. Ketcheson. Relaxation Runge--Kutta methods: Conservation and stabilityfor inner-product norms. SIAM Journal on Numerical Analysis, 57(6):2850--2870,2019.  [3] R. Abgrall. A general framework to construct schemes satisfyingadditional conservation relations. application to entropy conservative andentropy dissipative schemes. Journal of Computational Physics, 372:640--666,2018.

Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes