Reduced-order finite element method based on POD for fractional Tricomi-type equation. (English) Zbl 1342.65194
Summary: The reduced-order finite element method (FEM) based on a proper orthogonal decomposition (POD) theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save memory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element (FE) scheme is shown to be unconditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations (FDEs).
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
reduced-order finite element method (FEM); proper orthogonal decomposition (POD); fractional Tricomi-type equation; unconditionally stable; error estimateReferences:
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