Volume 9, Issue 1
A Uniformly Optimal-order Estimate for Bilinear Finite Element Method for Transient Advection-diffusion Equations

Q. Lin, K. Wang, H. Wang & X. Yin

DOI:

Int. J. Numer. Anal. Mod., 9 (2012), pp. 73-85

Published online: 2012-09

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  • Abstract

We prove an optimal-order error estimate in a weighted energy norm for bilinear Galerkin finite element method for two-dimensional timedependent advection-diffusion equations by the means of integral identities or expansions, in the sense that the generic constants in the estimates depend only on certain Sobolev norms of the true solution but not on the scaling parameter epsilon. These estimates, combined with a priori stability estimates of the governing partial differential equations, yield an "-uniform estimate of the bilinear Galerkin finite element method, in which the generic constants depend only on the Sobolev norms of the initial and right data but not on the scaling parameter epsilon.

  • Keywords

Convergence analysis Galerkin methods integral identity integral expansion uniform error estimates

  • AMS Subject Headings

65N15 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-73, author = {Q. Lin, K. Wang, H. Wang and X. Yin}, title = {A Uniformly Optimal-order Estimate for Bilinear Finite Element Method for Transient Advection-diffusion Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {1}, pages = {73--85}, abstract = {We prove an optimal-order error estimate in a weighted energy norm for bilinear Galerkin finite element method for two-dimensional timedependent advection-diffusion equations by the means of integral identities or expansions, in the sense that the generic constants in the estimates depend only on certain Sobolev norms of the true solution but not on the scaling parameter epsilon. These estimates, combined with a priori stability estimates of the governing partial differential equations, yield an "-uniform estimate of the bilinear Galerkin finite element method, in which the generic constants depend only on the Sobolev norms of the initial and right data but not on the scaling parameter epsilon.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/612.html} }
TY - JOUR T1 - A Uniformly Optimal-order Estimate for Bilinear Finite Element Method for Transient Advection-diffusion Equations AU - Q. Lin, K. Wang, H. Wang & X. Yin JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 73 EP - 85 PY - 2012 DA - 2012/09 SN - 9 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/ijnam/612.html KW - Convergence analysis KW - Galerkin methods KW - integral identity KW - integral expansion KW - uniform error estimates AB - We prove an optimal-order error estimate in a weighted energy norm for bilinear Galerkin finite element method for two-dimensional timedependent advection-diffusion equations by the means of integral identities or expansions, in the sense that the generic constants in the estimates depend only on certain Sobolev norms of the true solution but not on the scaling parameter epsilon. These estimates, combined with a priori stability estimates of the governing partial differential equations, yield an "-uniform estimate of the bilinear Galerkin finite element method, in which the generic constants depend only on the Sobolev norms of the initial and right data but not on the scaling parameter epsilon.
Q. Lin, K. Wang, H. Wang & X. Yin. (1970). A Uniformly Optimal-order Estimate for Bilinear Finite Element Method for Transient Advection-diffusion Equations. International Journal of Numerical Analysis and Modeling. 9 (1). 73-85. doi:
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