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The paper presents the Discontinuous Galerkin method (DG) formulated with a non-zero mesh skeleton width. The mesh skeleton has a finite volume but is not spatially discretized. Such an approach results in a novel formulation with inter-element interfaces which is named Interface Discontinuous Galerkin (IDG). The IDG approach, contrary to standard DG (SDG) approach, is symmetric and numerically stable. The IDG formulation is consistent and gives better results in comparison to the SDG method.doi:10.6084/m9.figshare.1304147.v1 fatcat:ajf77hcdgjf7fl3qkv6rdfbl4e