论文标题
使用矢量值的有限元素的局部衰减率，适用于规律性较低且可整合卷曲或发散的磁场元素
Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence
论文作者
论文摘要
我们使用矢量值有限元素估算最佳及其对分数Sobolev空间规模较低的字段的误差。通过另外假设目标场具有卷曲或发散性质，我们就可以在这些误差上建立上限，这些误差可以定位于网格细胞。这些边界是使用带有或没有边界处方的准插值误差来得出的。 Ern和J.-L.埃塞姆数学。模型。 numer。肛门，51（2017），pp。〜1367--1385]。通过使用[A. Ern和J.-L. Guermond，发现。计算。数学，（2021）]，并利用目标场卷曲或差异上的其他假设，得出了准交互误差上的局部上限。作为说明，我们展示了如何将这些结果应用于与麦克斯韦方程相关的卷曲卷曲问题的误差分析。
We estimate best-approximation errors using vector-valued finite elements for fields with low regularity in the scale of fractional-order Sobolev spaces. By assuming additionally that the target field has a curl or divergence property, we establish upper bounds on these errors that can be localized to the mesh cells. These bounds are derived using the quasi-interpolation errors with or without boundary prescription derived in [A. Ern and J.-L. Guermond, ESAIM Math. Model. Numer. Anal., 51 (2017), pp.~1367--1385]. By using the face-to-cell lifting operators analyzed in [A. Ern and J.-L. Guermond, Found. Comput. Math., (2021)], and exploiting the additional assumption made on the curl or the divergence of the target field, a localized upper bound on the quasi-interpolation error is derived. As an illustration, we show how to apply these results to the error analysis of the curl-curl problem associated with Maxwell's equations.
