论文标题
通过协变卷曲和regge指标不兼容分析曲率近似值
Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
论文作者
论文摘要
可以使用有限元元素近似riemannian歧管的度量张量，并且可以使用这种近似值来计算歧管的高斯曲率和Levi-Civita连接。结果表明，某些级别近似产生的曲率和连接近似值比以前已知的更高的速率收敛。该分析基于协变（分布）卷曲和不兼容运算符，可应用于分段平滑矩阵字段，其切向分类组件在元素界面之间是连续的。使用雷格空间的规范插值的特性，我们获得了这些协变量运算符的近似值的超授权。数值实验进一步说明了误差分析的结果。
The metric tensor of a Riemannian manifold can be approximated using Regge finite elements and such approximations can be used to compute approximations to the Gauss curvature and the Levi-Civita connection of the manifold. It is shown that certain Regge approximations yield curvature and connection approximations that converge at a higher rate than previously known. The analysis is based on covariant (distributional) curl and incompatibility operators which can be applied to piecewise smooth matrix fields whose tangential-tangential component is continuous across element interfaces. Using the properties of the canonical interpolant of the Regge space, we obtain superconvergence of approximations of these covariant operators. Numerical experiments further illustrate the results from the error analysis.
