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arXiv · 1610.05528

Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems

Peter Knabner·Gerhard Summ
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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.

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Peter Knabner, Gerhard Summ. 2016-10-18. Efficient Realization of the Mixed Finite Element Discretization for nonlinear Problems. https://arxiv.org/abs/1610.05528

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