论文标题
通过自适应有限元素对Griffith功能的离散近似
Discrete approximation of the Griffith functional by adaptive finite elements
论文作者
论文摘要
本文致力于显示出在断裂力学中产生的各向同性二维Griffith能量的离散自适应有限元近似结果。在几何量度测量界变形的特殊功能的理论框架中解决了该问题，该框架与该功能的自然能量空间相对应。事实证明，它是从$γ$ - 会议的意义上通过连续分段仿射函数定义的一系列离散积分函数来近似的。该结果的主要特征是网格是问题未知的一部分，并且具有足够的灵活性来恢复各向同性的表面能。
This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of generalized special functions of bounded deformation which corresponds to the natural energy space for this functional. It is proved to be approximated in the sense of $Γ$-convergence by a sequence of discrete integral functionals defined on continuous piecewise affine functions. The main feature of this result is that the mesh is part of the unknown of the problem, and it gives enough flexibility to recover isotropic surface energies.
