Kirchhoff板的自适应混合型C0不连续Galerkin方法的近似最优收敛率
Quasi-optimal convergence rate for an adaptive hybridizable C0 discontinuous Galerkin method for Kirchhoff plates
AI总结：
本文提出了一种用于Kirchhoff板的自适应混合型C0不连续Galerkin方法，并建立了可靠的后验误差估计器。通过后处理弯矩和离散霍尔姆霍兹分解，建立了准正交性和离散可靠性，研究了自适应方法的收缩性质和复杂度。
AI中文摘要：
本文提出了一种用于Kirchhoff板的自适应混合型C0不连续Galerkin（HCDG）方法。为该HCDG方法生成了一个可靠且高效的后验误差估计器。通过后处理的弯曲弯矩和离散霍尔姆霍兹分解，建立了准正交性和离散可靠性。基于这些，研究了两次循环之间的收缩性质和自适应HCDG方法的复杂度。分析中的关键点是来自HCDG方法解的后处理法向法向连续弯矩以及将间元边界处的跳跃残差提升到元内部。
英文摘要：
In this paper, we present an adaptive hybridizable $C^0$ discontinuous Galerkin (HCDG) method for Kirchhoff plates. A reliable and efficient a posteriori error estimator is produced for this HCDG method. Quasi-orthogonality and discrete reliability are established with the help of a postprocessed bending moment and the discrete Helmholtz decomposition. Based on these, the contraction property between two consecutive loops and complexity of the adaptive HCDG method are studied thoroughly. The key points in our analysis are a postprocessed normal-normal continuous bending moment from the HCDG method solution and a lifting of jump residuals from inter-element boundaries to element interiors.
