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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

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
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