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In this article, we show how to construct a numerical method for solvinghyperbolic problems, whether linear or nonlinear, using a continuousrepresentation of the variables and their mean value in each triangularelement. This type of approach has already been introduced by Roe, and others,in the multidimensional framework under the name of Active flux, see\cite{AF1,AF2,AF3,AF4,AF5}. Here, the presentation is more general and follows\cite{Abgrall_AF,BarzukowAbgrall}. { Various} examples show the good behaviorof the method in both linear and nonlinear cases, including non-convexproblems. The expected order of precision is obtained in both the linear andnonlinear cases. This work represents a step towards the development of methodsin the spirit of virtual finite elements for linear or nonlinear hyperbolicproblems, including the case where the solution is not regular.

Active flux for triangular meshes for compressible flows problems