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## Section: New Results

### High order approximations

Participants : Alain Dervieux, Bruno Koobus, Stephen Wornom, Tanya Kozubskaya [Keldysh Institute of Russian Academy] .

High order approximations for compressible flows on unstructured meshes are facing many constraints that increase their complexity i.e. their computational cost. This is clear for the largest class of approximation, the class of $k$-exact schemes, which rely on a local polynomial representation of degree $k$. We are investigating schemes which would solve as efficiently as possible the dilemma of choosing between an approximation with a representation inside macro-elements which finally constrains the mesh, and a representation around each individual cell, as in vertex formulations. This is a cooperation with the Keldysh Institute of Russian Academy which whom we have already developed several families of superconvergent schemes.