论文标题
vonKármán障碍问题的莫利有限元法
Morley Finite Element Method for the von Kármán Obstacle Problem
论文作者
论文摘要
本文重点介绍了vonKármán方程，以使非常薄的板的适度大变形具有凸障碍限制，从而导致半明律的四阶障碍物问题耦合系统，并激发了其不合格的莫利有限元近似。第一部分确定了vonKármán障碍物问题的良好性，还讨论了在数据上的先验和后验小度条件下解决方案的独特性。本文的第二部分讨论了1971年弗雷斯的规律性结果，并将其与溶液在多边形结构域上的规律性相结合。本文的第三部分显示了Morley有限元近似与VonKármán障碍物问题的最佳收敛率的先验误差估计。本文以数值结果结束，该结果说明了对数据对最佳收敛速率的规定的要求。
This paper focusses on the von Kármán equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilinear fourth-order obstacle problem and motivates its nonconforming Morley finite element approximation. The first part establishes the well-posedness of the von Kármán obstacle problem and also discusses the uniqueness of the solution under an a priori and an a posteriori smallness condition on the data. The second part of the article discusses the regularity result of Frehse from 1971 and combines it with the regularity of the solution on a polygonal domain. The third part of the article shows an a priori error estimate for optimal convergence rates for the Morley finite element approximation to the von Kármán obstacle problem for small data. The article concludes with numerical results that illustrates the requirement of smallness assumption on the data for optimal convergence rate.
