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A Residual-type A Posteriori Error Estimate of Finite Volume Element Method for a Quasi-linear Elliptic Problem

Abstract. In this paper, we analyze a residual-type a posteriori error estimator of the finite volume element method for a quasi-linear elliptic problem of nonmonotone type and derive computable upper and lower bounds on the error in the $H^1$-norm. Numerical experiments are provided to illustrate the performance of the proposed estimator.