Recursive POD Expansion for the Advection-Diffusion-Reaction Equation (Communications in Computational Physics, 2018)
This paper deals with the approximation of advection-diffusion-reactionequation solution by reduced order methods. We use the Recursive POD approximationfor multivariate functions introduced in [5] and applied to the low tensor representationof the solution of the reaction-diffusion partial differential equation. In thiscontribution we extend the Recursive POD approximation for multivariate functionswith an arbitrary number of parameters, for which we prove general error estimates.The method is used to approximate the solutions of the advection-diffusion-reactionequation. We prove spectral error estimates, in which the spectral convergence ratedepends only on the diffusion interval, while the error estimates are affected by a factorthat grows exponentially with the advection velocity, and are independent of thereaction rate if this lives in a bounded set. These error estimates are based upon theanalyticity of the solution of these equations as a function of the parameters (advectionvelocity, diffusion, reaction rate). We present several numerical tests, strongly consistentwith the theoretical error estimates.
Keywords: Reduced order methods; recursive POD; multivariate functions.