Semi-discrete Active Flux methods are shown to be Petrov-Galerkin schemes with discontinuous biorthogonal test functions, with explicit constructions for arbitrary order in one dimension and third order on Cartesian grids.
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Semi-discrete Active Flux as a Petrov-Galerkin method: the case of one-dimensional and Cartesian grids
Semi-discrete Active Flux methods are shown to be Petrov-Galerkin schemes with discontinuous biorthogonal test functions, with explicit constructions for arbitrary order in one dimension and third order on Cartesian grids.