A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems
Year: 2016
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 22–40
Abstract
In this paper, we consider the a posteriori error estimates of the finite volume element method for the general second-order quasilinear elliptic problems over a convex polygonal domain in the plane, propose a residual-based error estimator and derive the global upper and local lower bounds on the approximation error in the $H^1$-norm. Moreover, for some special quasilinear elliptic problems, we propose a residual-based a posteriori error estimator and derive the global upper bound on the error in the $L^2$-norm. Numerical experiments are also provided to verify our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2016-IJNAM-424
International Journal of Numerical Analysis and Modeling, Vol. 13 (2016), Iss. 1 : pp. 22–40
Published online: 2016-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: quasilinear elliptic problem finite volume element method a posteriori error estimates.