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DISCRETE HODGE-OPERATORS: AN ALGEBRAIC PERSPECTIVE

机译:离散杂散运算符:代数透视

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Discrete differential forms should be used to deal with the discretization of boundary value problems that can be stated in the calculus of differential forms. This approach preserves the topological features of the equations. Yet, the discrete counterparts of the metric-dependent constitutive laws remain elusive.rnI introduce a few purely algebraic constraints that matrices associated with discrete material laws have to satisfy. It turns out that most finite element and finite volume schemes comply with these requirements. Thus convergence analysis can be conducted in a unified setting. This discloses basic sufficient conditions that discrete material laws have to meet in order to ensure convergence in the relevant energy norms.
机译:离散微分形式应用于处理可以在微分形式的演算中说明的边值问题的离散化。这种方法保留了方程的拓扑特征。然而,与度量相关的本构定律的离散对等仍然难以捉摸。我引入了一些与离散材料定律相关的矩阵必须满足的纯代数约束。事实证明,大多数有限元和有限体积方案都符合这些要求。因此,可以在统一的设置中进行收敛分析。这公开了离散的材料定律必须满足的基本充分条件,以确保相关能量规范的收敛。

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