TY - JOUR
T1 - A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 22
EP - 40
PY - 2016
DA - 2016/01
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/424.html
KW - quasilinear elliptic problem, finite volume element method, a posteriori error estimates.
AB - <p style="text-align: justify;">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.</p>