An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity
Numerical Analysis
2020-07-30 v2 Numerical Analysis
Abstract
In this paper, we propose and analyze an abstract stabilized mixed finite element framework that can be applied to nonlinear incompressible elasticity problems. In the abstract stabilized framework, we prove that any mixed finite element method that satisfies the discrete inf-sup condition can be modified so that it is stable and optimal convergent as long as the mixed continuous problem is stable. Furthermore, we apply the abstract stabilized framework to nonlinear incompressible elasticity problems and present numerical experiments to verify the theoretical results.
Cite
@article{arxiv.2005.00189,
title = {An Abstract Stabilization Method with Applications to Nonlinear Incompressible Elasticity},
author = {Qingguo Hong and Chunmei Liu and Jinchao Xu},
journal= {arXiv preprint arXiv:2005.00189},
year = {2020}
}