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On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems. (English) Zbl 1340.65248
Summary: J. Karátson and S. Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type [Appl. Math., Praha 54, No. 4, 297–336 (2009; Zbl 1212.65249)]. The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the technical and numerical aspects and on the components of the error estimation, especially on the adequate solution of the involved auxiliary problem.
MSC:
65N15 Error bounds for boundary value problems involving PDEs
35J62 Quasilinear elliptic equations
65N06 Finite difference methods for boundary value problems involving PDEs
Software:
Maple; Matlab
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