A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
A mixed finite element method for nonlinear elasticity: two-fold saddle point approach and a-posteriori error estimate
复制标题
非线性弹性的混合有限元方法：二次鞍点法和后验误差估计
作者：
M. Barrientos;G. Gatica;E. Stephan
总结我们扩展的适用性稳定的混合有限元线性平面弹性，如PEERS，混合变分公式的超弹性。本方法是基于应变张量作为进一步的未知量，这产生了一个双重鞍点非线性算子方程相应的弱制定的介绍。我们给出了连续格式和离散格式解的唯一性，并给出了相应误差的一般Cea估计。最后，一个可靠的后验误差估计，局部Dirichlet问题的解决方案的基础上，以及适合于自适应计算，也给出了。
SummaryWe extend the applicability of stable mixed finite elements for linear plane elasticity, such as PEERS, to a mixed variational formulation of hyperelasticity. The present approach is based on the introduction of the strain tensor as a further unknown, which yields a two-fold saddle point nonlinear operator equation for the corresponding weak formulation. We provide the uniqueness of solution for the continuous and discrete schemes, and derive the usual Cea estimate for the associated error. Finally, a reliable a-posteriori error estimate, based on the solution of local Dirichlet problems, and well suited for adaptive computations, is also given.