A Stabilized Mixed Finite Element Method for Elliptic Systems of First Order

A quasilinear elliptic equation of second order can be split into a first order system in various ways. We present and analyze a stabilized finite element method for the system, which is well suited for any of these possible splittings. Under minimal assumptions on the continuous solution, existence...

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Published in:SIAM journal on numerical analysis 2005-01, Vol.43 (3), p.949-969
Main Authors: Dobrowolski, Manfred, Villegas, Manuel
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Language:English
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Eigenvalues
Finite element analysis
Methods
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description A quasilinear elliptic equation of second order can be split into a first order system in various ways. We present and analyze a stabilized finite element method for the system, which is well suited for any of these possible splittings. Under minimal assumptions on the continuous solution, existence and (nearly) optimal convergence in $L^\infty$ of the discrete solutions is established. This result holds for any choice of the stabilization parameter $\omega>0$. Moreover, the paper presents a framework for investigating other mixed methods for unsymmetric first order systems.
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subjects Eigenvalues
Finite element analysis
Methods
title A Stabilized Mixed Finite Element Method for Elliptic Systems of First Order
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