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Volume 27, Issue 2-3
An Anisotropic Nonconforming Finite Element Method for Approximating a Class of Nonlinear Sobolev Equations

Dongyang Shi, Haihong Wang & Yuepeng Du

J. Comp. Math., 27 (2009), pp. 299-314.

Published online: 2009-04

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  • Abstract

An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

  • Keywords

Nonlinear Sobolev equations, Anisotropic, Nonconforming finite element, Supercloseness, Global superconvergence.

  • AMS Subject Headings

65N30, 65N15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-299, author = {Dongyang Shi, Haihong Wang and Yuepeng Du}, title = {An Anisotropic Nonconforming Finite Element Method for Approximating a Class of Nonlinear Sobolev Equations}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {2-3}, pages = {299--314}, abstract = {

An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8574.html} }
TY - JOUR T1 - An Anisotropic Nonconforming Finite Element Method for Approximating a Class of Nonlinear Sobolev Equations AU - Dongyang Shi, Haihong Wang & Yuepeng Du JO - Journal of Computational Mathematics VL - 2-3 SP - 299 EP - 314 PY - 2009 DA - 2009/04 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8574.html KW - Nonlinear Sobolev equations, Anisotropic, Nonconforming finite element, Supercloseness, Global superconvergence. AB -

An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

Dongyang Shi, Haihong Wang and Yuepeng Du. (2009). An Anisotropic Nonconforming Finite Element Method for Approximating a Class of Nonlinear Sobolev Equations. Journal of Computational Mathematics. 27 (2-3). 299-314. doi:
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