Qualitatively Correct Discretizations in an Air Pollution Model
We deal with one subproblem of an air pollution model, the horizontal diffusion, which can be mathematically described by a linear partial differential equation of parabolic type. With different space discretization schemes (like a FDM, FEM), and using the θ-method for time discretization we get a one-step algebraic iteration as a numerical model. The preservation of characteristic qualitative properties of different phenomena is an increasingly important requirement in the construction of reliable numerical models. For that reason we analyze the connection between the shape and time-monotonicity in the continuous and the numerical model, and we give the necessary and sufficient condition to fulfil this property.
KeywordsDiscrete Model Time Level Discrete Maximum Principle Matrix Splitting Regular Splitting
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