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A Douglas-Wang finite element approach for transient advection-diffusion problems. (English) Zbl 0845.76044
The paper presents an effective finite element method for approximating the two-dimensional unsteady advection-diffusion transport. The new scheme is a direct generalization of the Douglas-Wang finite element method applied to steady advection-diffusion and Stokes problems. Higher-order spatial derivatives in the new formulation necessitate higher-degree polynomial shape function. Quadratic finite element approximation (quadrilateral \(Q9\) and triangular \(T6\)) are used. The finite difference \(\theta\)-weighting formulation is used for a time discretization. A stability analysis, using the von Neumann method, shows that the formulation based on the implicit Crank-Nicholson scheme reduces dissipation and dispersion errors when both advective and diffusive problems are considered.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76R50 Diffusion
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