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Operator-splitting method for high-dimensional parabolic equation via finite element method. (English) Zbl 1399.65264

Summary: This work introduces a new operator-splitting method for solving the two-dimensional (2D) and three-dimensional (3D) parabolic equations. The aim is to reduce the computational complexity without loss of accuracy. Firstly, we split the 2D and 3D parabolic equations into a sequence of one-dimensional (1D) parabolic equations respectively, then we solve each 1D parabolic equation by using finite element method. In comparison with standard finite element method, the present method can save much CPU time. Furthermore, the stability analysis and error estimates for the proposed method are derived. Finally, numerical results of the 2D and 3D parabolic equations are presented to support our theoretical analysis.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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