A Discontinuous Galerkin type method written in Lagrangian coordinates is described in this work for unstructured meshes in 1D/2D for the Euler equations. By using Bernstein polynomials a diffusive process has been added to stabilize the method. Thanks to this process the Jacobian positivity is preserved during the computation ensuring the validity of the transformation from Euler coordinates to Lagrangian coordinates. The moment equations by respect to the Bernstein basis are solved. A Rieman solver (on moments) is used to treat the discontinuities between cells. Some numerical examples in compressible fluid dynamics show the efficiency of the method.