论文标题
多项式射击H（卷曲） - 四面体中离散最小化的稳定性
Polynomial-degree-robust H(curl)-stability of discrete minimization in a tetrahedron
论文作者
论文摘要
我们证明，离散最小化问题的一定程度p> 0的Nédélec多项式空间中的最小化器以及H（卷曲）中的连续最小化器，直至与多项式程度p无关的常数。对于在R^3中的单个非脱位四面体上定义的场提出了最小化问题，并在磁场的卷发上强制执行多项式约束，其切向痕迹在四面体的某些面上。该结果建立在[L. Demkowicz，J。Gopalakrishnan，J。SchöberlSiam J. Numer。肛门。 47（2009），3293--3324]和[M. Costabel，A。McIntosh，数学。 Z. 265（2010），297--320]，是构建多项式射击的基本要素，当时在几个方案中近似Maxwell方程式，导致卷曲curl问题时，后验误差估计器。
We prove that the minimizer in the Nédélec polynomial space of some degree p > 0 of a discrete minimization problem performs as well as the continuous minimizer in H(curl), up to a constant that is independent of the polynomial degree p. The minimization problems are posed for fields defined on a single non-degenerate tetrahedron in R^3 with polynomial constraints enforced on the curl of the field and its tangential trace on some faces of the tetrahedron. This result builds upon [L. Demkowicz, J. Gopalakrishnan, J. Schöberl SIAM J. Numer. Anal. 47 (2009), 3293--3324] and [M. Costabel, A. McIntosh, Math. Z. 265 (2010), 297--320] and is a fundamental ingredient to build polynomial-degree-robust a posteriori error estimators when approximating the Maxwell equations in several regimes leading to a curl-curl problem.
