TY - JOUR
T1 - Construction of Boundary Layer Elements for Singularly Perturbed Convection-Diffusion Equations and $L^2$-Stability Analysis
AU - C.-Y. Jung & R. Temam
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 729
EP - 748
PY - 2008
DA - 2008/05
SN - 5
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/835.html
KW - boundary layer, boundary layer element, finite elements, singularly perturbed problem, convection-diffusion, stability, enriched subspaces, exponentially fitted splines.
AB - <p style="text-align: justify;">It has been demonstrated that the ordinary boundary layer
elements play an essential role in the finite element approximations for
singularly perturbed problems producing ordinary boundary layers. Here
we revise the element so that it has a small compact support and hence
the resulting linear system becomes sparse, more precisely, block
tridiagonal. We prove the validity of the revised element for some
singularly perturbed convection-diffusion equations via numerical
simulations and via the $H^1$-approximation error analysis. Furthermore
due to the compact structure of the boundary layer we are able to prove
the $L^2$-stability analysis of the scheme and derive the $L^2$-error
approximations.</p>