A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

Simone Brugiapaglia, Fabio Nobile, Stefano Micheletti, Simona Perotto
2017 Mathematics of Computation  
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 and
more » ... selected trial and test bases fulfills suitable decay properties. The fundamental tool of this analysis is the restricted infsup property, i.e., a combination of the classical inf-sup condition and the well-known restricted isometry property of compressed sensing.
doi:10.1090/mcom/3209 fatcat:ook4rkoms5de3d3yzvl5ibenku