×

zbMATH — the first resource for mathematics

Mixed finite element methods for quasilinear second-order elliptic problems. (English) Zbl 0567.65079
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, \bu and \({\underline \nabla}.u\) where \bu\(=-a(p){\underline \nabla}p+\underline b(p)\). 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
PDF BibTeX XML Cite
Full Text: DOI