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

C.-J. Bi & C. Wang

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

Published online: 2016-01

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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 $H^1$-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.

  • Keywords

quasilinear elliptic problem, finite volume element method, a posteriori error estimates.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-13-22, author = {C.-J. Bi and C. Wang}, title = {A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2016}, volume = {13}, number = {1}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/424.html} }
TY - JOUR T1 - A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems AU - C.-J. Bi & C. Wang 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 -

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.

C.-J. Bi and C. Wang. (2016). A Posteriori Error Estimates of Finite Volume Element Method for Second-Order Quasilinear Elliptic Problems. International Journal of Numerical Analysis and Modeling. 13 (1). 22-40. doi:
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