Continuous/Discontinuous Galerkin Difference Discretizations of High-Order Differential Operators
Continuous/Discontinuous Galerkin Difference Discretizations of High-Order Differential Operators
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DOI：
10.1007/s10915-022-01891-y
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发表时间：
2022-06
影响因子：
2.5
通讯作者：
J. Banks;B. B. Buckner-B.;T. Hagstrom
中科院分区：
文献类型：
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作者：
J. Banks;B. B. Buckner-B.;T. Hagstrom
我们开发连续/不连续离散高阶微分算子使用伽辽金差分方法。网格色散分析表明，在thumm节点超收敛。的边界条件的处理，最终导致适度增长的多项式度的运营商的谱半径，并在一般情况下的Galerkin差分微分算子的规范显着小于标准元素所产生的。最后，我们观察到，使用的Galerkin差分空间，离散高阶算子所需的标准惩罚项是不需要的。数值结果证实了分析的结论。
We develop continuous/discontinuous discretizations for high-order differential operators using the Galerkin Difference approach. Grid dispersion analyses are performed that indicate a nodal superconvergence in thenorm. A treatment of the boundary conditions is described that ultimately leads to moderate growth in the spectral radius of the operators with polynomial degree, and in general the norms of the Galerkin Difference differentiation operators are significantly smaller than those arising from standard elements. Lastly, we observe that with the use of the Galerkin Difference space, the standard penalty terms required for discretizing high-order operators are not needed. Numerical results confirm the conclusions of the analyses performed.