Abstract

Convective transport in convection–diffusion problems can be formulated differently. Convective terms are commonly written in nondivergent or divergent form. For problems of this type, monotone and stable schemes in Banach spaces are constructed in uniform and integral norms, respectively. Monotonicity is related to row or column diagonal dominance. When convective terms are written in symmetric form (the half-sum of the nondivergent and divergent forms), the stability is established in Hilbert spaces of grid functions. Diagonal dominance conditions are given that ensure the monotonicity of two-level schemes for time-dependent convection–diffusion equations and the stability in corresponding spaces.

中文翻译：

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对流传输形式不同的对流扩散问题的单调方案

摘要

对流扩散问题中的对流输运可以用不同的公式表述。对流术语通常以非趋异或趋异形式书写。对于此类问题，Banach空间中的单调方案和稳定方案分别以统一和整数范数构造。单调性与行或列的对角线优势有关。当对流项以对称形式（非发散和发散形式的一半和）书写时，在网格函数的希尔伯特空间中建立了稳定性。给出了对角支配条件，该条件可确保两类时变对流扩散方程的单调性，并确保其在相应空间中的稳定性。