论文标题
障碍物问题解决方案的数值近似，通过惩罚方法对椭圆膜壳的位移进行建模
Numerical approximation of the solution of an obstacle problem modelling the displacement of elliptic membrane shells via the penalty method
论文作者
论文摘要
在本文中，我们建立了基于有限元方法的数值方案的收敛性，用于建模时间无关的问题，该问题对线性弹性的椭圆形膜壳的变形进行建模，该壳壳被限制在半空间中。我们没有估算有关此障碍问题的原始变异不平等，而是近似所考虑的问题的惩罚版本。然后，惩罚参数和网格大小之间的合适耦合将使我们确定离散惩罚问题解决方案与原始变异不平等解决方案的融合。我们还为正在考虑的问题建立了布雷兹 - 苏比尼方案的融合。借助这种迭代方法，我们可以近似于离散刑罚问题的解决方案，而无需诉诸于非线性优化工具。最后，我们提出数值模拟，以验证我们的新理论结果。
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in a half space. Instead of approximating the original variational inequalities governing this obstacle problem, we approximate the penalized version of the problem under consideration. A suitable coupling between the penalty parameter and the mesh size will then lead us to establish the convergence of the solution of the discrete penalized problem to the solution of the original variational inequalities. We also establish the convergence of the Brezis-Sibony scheme for the problem under consideration. Thanks to this iterative method, we can approximate the solution of the discrete penalized problem without having to resort to nonlinear optimization tools. Finally, we present numerical simulations validating our new theoretical results.
