A stabilized mixed finite element method for elliptic systems of first order

摘要

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-infinity 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.