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This article considers a new discretization scheme for conservation laws. Thediscretization setting is based on a discontinuous Galerkin scheme incombination with an approximation space that contains high-order polynomialmodes as well as piece-wise constant modes on a sub-grid. The high-order modescan continuously be suppressed with a penalty function that is based on asensor which is intertwined with the approximation space. Numerical testsfinally illustrate the performance of this scheme.

A Discontinuous Galerkin method for Shock Capturing using a mixed high-order and sub-grid low-order approximation space