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We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a PDE with respect to an orthonormal system of N trial functions, can be recovered via a Petrov-Galerkin approach using m N orthonormal test functions. This recovery is guaranteed if the local a-coherence associated with the bilinear form anddoi:10.1090/mcom/3209 fatcat:ook4rkoms5de3d3yzvl5ibenku