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Flux reconstruction and solution post-processing in mimetic finite difference methods

机译:模拟有限差分法的通量重构和解后处理

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We present a post-processing technique for the mimetic finite difference solution of diffusion problems in mixed form. Our postprocessing method yields a piecewise linear approximation of the scalar variable that is second-order accurate in the L~2-norm on quite general polyhedral meshes, including non-convex and non-matching elements. The post-processing is based on the reconstruction of vector fields projected onto the mimetic space of vector variables. This technique is exact on constant vector fields and is shown to be independent of the mimetic scalar product choice if a local consistency condition is satisfied. The post-processing method is computationally inexpensive. Optimal performance is confirmed by numerical experiments.
机译:我们为混合形式的扩散问题的模拟有限差分解决方案提供了一种后处理技术。我们的后处理方法产生了标量变量的分段线性逼近,在相当普通的多面体网格(包括非凸和非匹配元素)上,L〜2-范数中的标量变量是二阶精确的。后处理基于投影到矢量变量模拟空间上的矢量场的重构。该技术在恒定向量场上是精确的,并且如果满足局部一致性条件,则表明它与模拟标量积选择无关。后处理方法在计算上不昂贵。数值实验证实了最佳性能。

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