Volume 13, Issue 1
A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems

C.-J. Bi and C. Wang

Int. J. Numer. Anal. Mod., 13 (2016), pp. 22-40

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  • 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 H¹-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 L²-norm. Numerical experiments are also provided to verify our theoretical results.

  • History

Published online: 2016-01

  • AMS Subject Headings

65N15, 65N30

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