Sandpiles and superconductors: nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities
Sandpiles and superconductors: nonconforming linear finite element approximations for mixed formulations of quasi-variational inequalities
复制标题
沙堆和超导体：拟变分不等式混合公式的非相容线性有限元近似
DOI：
10.1093/imanum/drt062
复制
发表时间：
2013
影响因子：
2.1
通讯作者：
L. Prigozhin
中科院分区：
文献类型：
--
作者：
J. Barrett;L. Prigozhin
类似的演化变分和准变分不等式梯度约束出现在不断增长的沙堆和II型超导体的建模。最近，这些不等式的混合配方用于建立存在性结果的拟变分不等式的情况下。这样的公式，这是一个额外的优点，使得有可能不仅在数字上确定原始变量，演变的沙堆和超导体的砂表面和磁场，分别，而且双变量，砂通量和电场。在以前的研究中，这些混合配方的数值近似采用了最低阶的Raviart-Thomas元素。在这里，我们介绍了更简单的数值逼近这些混合配方的基础上的非线性有限元。我们证明了这些近似的收敛性，并通过数值实验说明了它们的有效性。
Similar evolutionary variational and quasi-variational inequalities with gradient constraints arise in the modelling of growing sandpiles and type-II superconductors. Recently, mixed formulations of these inequalities were used for establishing existence results in the quasi-variational inequality case. Such formulations, and this is an additional advantage, made it possible to determine numerically not only the primal variables, e.g., the evolving sand surface and the magnetic field for sandpiles and superconductors, respectively, but also the dual variables, the sand flux and the electric field. Numerical approximations of these mixed formulations in previous studies employed the Raviart–Thomas element of the lowest order. Here we introduce simpler numerical approximations of these mixed formulations based on the nonconforming linear finite element. We prove (subsequence) convergence of these approximations and illustrate their effectiveness by numerical experiments.