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Volume 20, Issue 6
Finite Element Methods for Sobolev Equations

Liu Tang, Shu-Hua Zhang, J. R. Cannon, Yan-Ping Lin & Ming Rao

J. Comp. Math., 20 (2002), pp. 627-642.

Published online: 2002-12

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  • Abstract

A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.

  • Keywords

Error estimates, finite element, Sobolev equation, numerical integration.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-627, author = {Tang , LiuZhang , Shu-HuaCannon , J. R.Lin , Yan-Ping and Rao , Ming}, title = {Finite Element Methods for Sobolev Equations}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {627--642}, abstract = {

A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8948.html} }
TY - JOUR T1 - Finite Element Methods for Sobolev Equations AU - Tang , Liu AU - Zhang , Shu-Hua AU - Cannon , J. R. AU - Lin , Yan-Ping AU - Rao , Ming JO - Journal of Computational Mathematics VL - 6 SP - 627 EP - 642 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8948.html KW - Error estimates, finite element, Sobolev equation, numerical integration. AB -

A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method are derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.

Tang , LiuZhang , Shu-HuaCannon , J. R.Lin , Yan-Ping and Rao , Ming. (2002). Finite Element Methods for Sobolev Equations. Journal of Computational Mathematics. 20 (6). 627-642. doi:
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