@Article{IJNAM-9-1,
author = {},
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 = {<p style="text-align: justify;">We prove an optimal-order error estimate in a weighted energy
norm for bilinear Galerkin finite element method for two-dimensional time-dependent
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 $\varepsilon$. These estimates, combined with a priori stability estimates of
the governing partial differential equations, yield an &quot;$\varepsilon$-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 $\varepsilon$.</p>},
issn = {2617-8710},
doi = {https://doi.org/2012-IJNAM-612},
url = {https://global-sci.com/article/83453/a-uniformly-optimal-order-estimate-for-bilinear-finite-element-method-for-transient-advection-diffusion-equations}
}