Mixed finite element methods for quasilinear second-order elliptic problems. (English) Zbl 0567.65079

Milner, F. A.

Math. Comput. 44, 303-320 (1985).

The author considers the problem defined by \(-{\underline \nabla}[a(p){\underline \nabla}p+\underline b(p)]+c(p)=f\) in \(\Omega\), \(p=-g\) on \(\partial \Omega\). He develops a mixed finite element method to approximate the solution, and proves that the solution exists uniquely. He obtains error estimates for approximations for p, \b{u} and \({\underline \nabla}.u\) where \b{u}\(=-a(p){\underline \nabla}p+\underline b(p)\). The treatment is highly abstract and there is no application to concrete examples.

Reviewer: Ll.G.Chambers

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
35J65	Nonlinear boundary value problems for linear elliptic equations

Keywords:

quasilinear second-order; mixed finite element method; error estimates