Convergence rates of the DPG method with reduced test space degree

Convergence rates of the DPG method with reduced test space degree
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DOI：
10.1016/j.camwa.2014.08.004
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发表时间：
2014-08
期刊：
Comput. Math. Appl.
影响因子：
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通讯作者：
T. Bouma;Jay Gopalakrishnan;A. Harb
T. Bouma;Jay Gopalakrishnan;A. Harb
中科院分区：
其他
文献类型：
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作者：
T. Bouma;Jay Gopalakrishnan;A. Harb

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本文给出了间断Petrov-Galerkin（DPG）方法的Aubin-Nitsche型对偶定理。这解释了在较弱的规范下数值上观察到的较高收敛速率。考虑拉普拉斯方程的弱（或原始）DPG方法的具体例子，得到了两个进一步的结果.首先，即使测试空间度减少，只要它是奇数，DPG方法仍然是可解的。其次，一个非协调的分析方法来解释数值观察到的收敛速度的测试空间的减少程度。
This paper presents a duality theorem of the Aubin–Nitsche type for discontinuous Petrov–Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree.