Chapter 9: Parabolic Problems
Axel Målqvist, Daniel Peterseim · Society for Industrial and Applied Mathematics eBooks · 2020
Parabolic multiscale problems arise in many applications, including heat transfer in heterogeneous materials and modeling of pressure in porous media flow. In this chapter we will use the LOD method as a spatial discretization technique when solving the linear heat equation with multiscale diffusion. Since the diffusion coefficient is independent of time, we will be able to reuse the LOD correctors throughout the simulation, resulting in a significant speed-up compared to a direct simulation of the global problem. We will show that the LOD approximation converges with optimal rate independent of the variations in the diffusion both theoretically and numerically.