Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems
Numerical Analysis
2016-10-19 v1
Abstract
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite element method with augmented Crouzeix-Raviart ansatz space. We discuss the reduction of unknowns by static condensation and propose Newton's method for the solution of local and global systems. Finally, we show, how such a nonlinear problem arises from the mixed formulation of Darcy-Forchheimer flow in porous media.
Cite
@article{arxiv.1610.05528,
title = {Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems},
author = {Peter Knabner and Gerhard Summ},
journal= {arXiv preprint arXiv:1610.05528},
year = {2016}
}