Two-Grid based Adaptive Proper Orthogonal Decomposition Algorithm for Time Dependent Partial Differential Equations

Abstract: In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for the numerical solution obtained in the fine grid. Our new algorithm is cheap and easy to be implement. We apply our new method to the solution of time-dependent advection-diffusion equations with the Kolmogorov flow and the ABC flow. The numerical results show that our method is more efficient than the existing POD methods.