稳定化有限元 $\theta$ 格式求解非定常对流占优扩散方程

Abstract

Abstract:

This paper proposes a fully discrete $\theta$ scheme with the variational multiscale finite element method for non-stationary convection-dominated convection diffusion equations. We use an equivalent method based on the residuals of two local Gauss integrations to replace the stabilization term of the variational multiscale method. An optimal error estimate in the space-time $L^2$ norm is also derived. Moreover, numerical results demonstrate that equivalent numerical accuracy can be achieved by the Crank-Nicolson scheme with lower computational cost compared to the Backward Euler scheme.

Key words: convection-dominated convection diffusion equations, variational multiscale method, stabilized finite element method, two local Gauss integrations.

CLC Number:

O241.82

Lanxin Sun, Baowei Lai, Zhifeng Weng. A Stabilized Finite Element $\theta$ Scheme for Non-Stationary Convection-Dominated Convection Diffusion Problems[J].Acta mathematica scientia,Series A, 2026, 46(3): 1218-1231.

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References 24

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A Stabilized Finite Element $\theta$ Scheme for Non-Stationary Convection-Dominated Convection Diffusion Problems

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