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1998•Journal of Korea Water Resources AssociationRequires access

Optimal Test Function Petrov-Galerkin Method

Sung-Uk Choi

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Abstract

Numerical analysis of convection-dominated transport problems are challenging because of dual characteristics of the governing equation. In the finite element method, a strategy is to modify the test function to weight more in the upwind direction. This is called as the Petrov-Galerkin method. In this paper, both N+1 and N+2 Petrov-Galerkin methods are applied to transport problems at high grid Peclet number. Frequency fitting algorithm is used to obtain optimal levels of N+2 upwinding, and the results are discussed. Also, a new Petrov-Galerkin method, named as Optimal Test Function Petrov-Galerkin Method, is proposed in this paper. The test function of this numerical method changes its shape depending upon relative strength of the convection to the diffusion. A numerical experiment is carried out to demonstrate the performance of the proposed method.

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What this paper is about

Numerical analysis of convection-dominated transport problems are challenging because of dual characteristics of the governing equation. In the finite element method, a strategy is to modify the test function to weight more in the upwind direction. This is called as the Petrov-Galerkin method. In this paper, both N+1 and N+2 Petrov-Galerkin methods are applied to transport problems at high grid Peclet number. Frequency fitting algorithm is used to obtain optimal levels of N+2 upwinding, and the results are discussed. Also, a new Petrov-Galerkin method, named as Optimal Test Function Petrov-Galerkin Method, is proposed in this paper. The test function of this numerical method changes its shape depending upon relative strength of the convection to the diffusion. A numerical experiment is carried out to demonstrate the performance of the proposed method.

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Available abstract

Numerical analysis of convection-dominated transport problems are challenging because of dual characteristics of the governing equation. In the finite element method, a strategy is to modify the test function to weight more in the upwind direction. This is called as the Petrov-Galerkin method. In this paper, both N+1 and N+2 Petrov-Galerkin methods are applied to transport problems at high grid Peclet number. Frequency fitting algorithm is used to obtain optimal levels of N+2 upwinding, and the results are discussed. Also, a new Petrov-Galerkin method, named as Optimal Test Function Petrov-Galerkin Method, is proposed in this paper. The test function of this numerical method changes its shape depending upon relative strength of the convection to the diffusion. A numerical experiment is carried out to demonstrate the performance of the proposed method.

Key concepts: Petrov–Galerkin method, Convection–diffusion equation, Galerkin method, Mathematics, Upwind scheme, Finite element method, Applied mathematics, Function (biology)

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