Volume 20, Issue 6
Finite Element Methods for Sobolev Equations

Tang Liu, Yan Ping Lin, Ming Rao & J. R. Cannon

DOI:

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. Theoptimal 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 tinite element method is demonstrates can be bounded by the noums 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

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@Article{JCM-20-627, author = {}, 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. Theoptimal 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 tinite element method is demonstrates can be bounded by the noums 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 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 KW - finite element KW - Sobolev equation KW - 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. Theoptimal 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 tinite element method is demonstrates can be bounded by the noums of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Tang Liu, Yan Ping Lin, Ming Rao & J. R. Cannon. (1970). Finite Element Methods for Sobolev Equations. Journal of Computational Mathematics. 20 (6). 627-642. doi:
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