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...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on numerical analysis 2005-01, Vol.43 (3), p.949-969
Main Authors: Dobrowolski, Manfred, Villegas, Manuel
Format: Article
Language:English
Subjects:
Eigenvalues
Finite element analysis
Methods
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0036-1429
1095-7170
DOI:10.1137/S0036142902408829