HiMod Reduction of Advection–Diffusion–Reaction Problems with General Boundary Conditions

We extend the hierarchical model reduction procedure previously introduced in Ern et al. (in: Kunisch, Of, Steinbach (eds) Numerical mathematics and advanced applications, Springer, Berlin, pp 703–710, 2008) and Perotto et al. (Multiscale Model Simul 8(4):1102–1127, 2010) to deal with general boundary conditions, enforcing their prescription in the basis function set. This is achieved by solving a Sturm–Liouville Eigenvalue problem. We analyze this approach and provide a convergence analysis for the associated error in the case of a linear advection–diffusion–reaction problem in rectangles (2D) and slabs (3D). Numerical results confirm the theoretical investigation and the reliability of the proposed approach.