论文标题
稳定的断裂H（卷曲）多项式扩展和p-robust curl-curl问题的斑块平衡估计后验错误估计
Stable broken H(curl) polynomial extensions and p-robust a posteriori error estimates by broken patchwise equilibration for the curl-curl problem
论文作者
论文摘要
我们研究在具有边缘的四面体中规定的分段多项式数据的扩展。从某种意义上说，在分段多项式空间上，我们表现出稳定性，这些空间具有规定的切向组件在面上跳跃，并且在元素中处方的分段卷发在破碎的能量标准中服从于损坏的h（curl）空间上的最小化器。我们的证明是独立于多项式程度的建设性和产量常数。然后，我们将此结果的应用详细介绍了通过任意顺序的Nédélec有限元离散的卷曲 - 折曲问题的后验错误分析。所得的估计量是可靠的，局部高效的，多项式的，并且廉价。它们是由碎片平衡构造的，尤其是不会产生全球h（卷曲）符合通量的通量。平衡仅与边缘斑块有关，并且可以通过绕过每个网格边缘的四面体，而无需解决斑块问题的解决方案。当规则拾取常数明确已知时，将保证误差估计值。数值实验说明了理论发现。
We study extensions of piecewise polynomial data prescribed in a patch of tetrahedra sharing an edge. We show stability in the sense that the minimizers over piecewise polynomial spaces with prescribed tangential component jumps across faces and prescribed piecewise curl in elements are subordinate in the broken energy norm to the minimizers over the broken H(curl) space with the same prescriptions. Our proofs are constructive and yield constants independent of the polynomial degree. We then detail the application of this result to the a posteriori error analysis of the curl-curl problem discretized with Nédélec finite elements of arbitrary order. The resulting estimators are reliable, locally efficient, polynomial-degree-robust, and inexpensive. They are constructed by a broken patchwise equilibration which, in particular, does not produce a globally H(curl)-conforming flux. The equilibration is only related to edge patches and can be realized without solutions of patch problems by a sweep through tetrahedra around every mesh edge. The error estimates become guaranteed when the regularity pick-up constant is explicitly known. Numerical experiments illustrate the theoretical findings.
