An augmented subspace based adaptive proper orthogonal decomposition method for time dependent partial differential equations. (English) Zbl 07899001
Summary: In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. We use the difference between the approximation obtained in the augmented subspace and that obtained in the original POD subspace to construct an error indicator, by which we obtain a general framework for augmented subspace based adaptive POD method. We then provide two strategies to construct the augmented subspaces, the residual type augmented subspace and the coarse-grid approximation type augmented subspace. We apply our new methods to two typical 3D advection-diffusion equations with the advection being the Kolmogorov flow and the ABC flow. Numerical results show that both the residual type augmented subspace based adaptive POD method and the coarse-grid approximation type augmented subspace based adaptive POD method are more efficient than the existing adaptive POD methods, especially for the advection dominated models.
MSC:
| 65Mxx | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 35Kxx | Parabolic equations and parabolic systems |
Keywords:
proper orthogonal decomposition; adaptive; augmented subspace; Galerkin projection; error indicatorReferences:
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