On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method
On the Connection Between the Correction and Weighting Functions in the Correction Procedure via Reconstruction Method
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DOI：
10.1007/s10915-012-9618-3
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发表时间：
2013
影响因子：
2.5
通讯作者：
Meilin Yu;Z. Wang
中科院分区：
文献类型：
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作者：
Meilin Yu;Z. Wang
在这篇笔记中，校正和加权函数之间的联系，通过重建（CPR）方法在1D中的校正过程中解决。从不连续的测试空间构造了一个单参数的加权函数族。我们发现，如果解多项式位于空间Pk中，那么前k个加权函数总是可以被选为多项式空间Pk − 1的基，而最后一个加权函数可以被选为分段连续多项式。存在至少一组权函数，可以恢复能量稳定通量重建（ESFR）方案。该策略已成功地应用于恢复几个已知的高阶间断格式，包括DG，SD，SV和Huynh的sg2格式。
In this note, the connection between the correction and weighting functions for the correction procedure via reconstruction (CPR) method in 1D is addressed. A one-parameter family of weighting functions is constructed from the discontinuous test space. It is found that if the solution polynomials lie in the spacePk, then the firstkweighting functions can always be chosen as the basis of the polynomial spacePk−1and the last weighting function can be selected as a piece-wise continuous polynomial. There exists at least one set of weighting functions which can recover the energy stable flux reconstruction (ESFR) schemes. This strategy has been successfully applied to recover several known high-order discontinuous schemes, including DG, SD, SV, and Huynh’sg2scheme.