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- Title
A Reduced Order Local Discontinuous Galerkin Method for the Variable Coefficients Diffusion Equations.
- Authors
Danchen Zhu; Lingzhi Qian; Jing Wang
- Abstract
In this paper, the model reduction technique is applied to solve the variable coefficients diffusion equation. In the full order model (FOM), we use Crank-Nicolson (CN) method and local discontinuous Galerkin (LDG) method to discretize the variable coefficients diffusion equation. To construct the reduced order model (ROM), we use the proper orthogonal decomposition (POD) method and the Galerkin projection to reduce the number of unknowns in the FOM. Similar to FOM, the LDG method still can reach the optimal convergence in the ROM. At the same time, the ROM can provide accurate approximate solution of the variable coefficients diffusion equation with much less computational cost. Finally, some numerical tests are illustrated to confirm the performance of the proposed reduction method.
- Subjects
HEAT equation; DIFFUSION coefficients; GALERKIN methods; PROPER orthogonal decomposition; REDUCED-order models; REACTION-diffusion equations; CRANK-nicolson method; DISCONTINUOUS functions
- Publication
IAENG International Journal of Applied Mathematics, 2023, Vol 53, Issue 4, p1370
- ISSN
1992-9978
- Publication type
Article