A residual-type a posteriori error estimate of finite volume element method for a quasi-linear elliptic problem. (English) Zbl 1187.65121
The aim of this paper is to study the residual-type a posteriori error estimates of the finite volume element (FVE) method for a quasi-linear elliptic problem of nonmonotone type. The authors give an error representation of the FVE method, which reveals the relationship between the FVE and the finite element method and get computable upper and lower bounds on the error in the \(H^1\)-norm. The paper concludes with supporting numerical experiments.
Reviewer: Nicolae Pop (Baia Mare)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N08 | Finite volume methods for boundary value problems involving PDEs |
| 35J62 | Quasilinear elliptic equations |
Keywords:
posteriori error estimates; finite volume element method; quasi-linear elliptic problem; numerical experiments; error boundsReferences:
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