TY - JOUR
T1 - An Enriched Subspace Finite Element Method for Convection-Diffusion Problems
AU - R. B. Kellogg & C. Xenophontos
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 477
EP - 490
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/732.html
KW - Finite element method, boundary layers, enriched subspace.
AB - <p style="text-align: justify;">We consider a one-dimensional convection-diffusion boundary value
problem, whose solution contains a boundary layer at the outflow boundary,
and construct a finite element method for its approximation. The finite element
space consists of piecewise polynomials on a uniform mesh but is enriched by
a finite number of functions that represent the boundary layer behavior. We
show that this method converges at the optimal rate, independently of the
singular perturbation parameter, when the error is measured in the energy
norm associated with the problem. Numerical results confirming the theory
are also presented, which also suggest that in the case of variable coefficients,
the number of enrichment functions need not be as high as the theory suggests.</p>