论文标题
立方网格上差异形式的新自由度
New degrees of freedom for differential forms on cubical meshes
论文作者
论文摘要
我们考虑了立方网格上高阶差异形式的新自由度。这种方法的灵感来自Rapetti和Bossavit的想法，即使用小简单来定义高级惠特尼形式及其自由度。我们表明，可以使用小立方体来定义立方网格上的高阶差分形式，并证明这些小立方体产生了单回散的自由度。值得注意的是，这种方法与离散的外部微积分兼容，并扩展了框架以涵盖立方网格上的高阶方法，从而补充了基于简单的早期策略。
We consider new degrees of freedom for higher order differential forms on cubical meshes. The approach is inspired by the idea of Rapetti and Bossavit to define higher order Whitney forms and their degrees of freedom using small simplices. We show that higher order differential forms on cubical meshes can be defined analogously using small cubes and prove that these small cubes yield unisolvent degrees of freedom. Significantly, this approach is compatible with discrete exterior calculus and expands the framework to cover higher order methods on cubical meshes, complementing the earlier strategy based on simplices.
