TY - JOUR
T1 - An $hp$ Finite Element Method for a Singularly Perturbed Reaction-Convection-Diffusion Boundary Value Problem with Two Small Parameters
AU - Sykopetritou , ​Irene
AU - Xenophontos , Christos
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 481
EP - 499
PY - 2021
DA - 2021/05
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/19111.html
KW - Singularly perturbed problem, reaction-convection-diffusion, boundary layers, $hp$
finite element method, robust exponential convergence.
AB - <p style="text-align: justify;">We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called $Spectral$ $Boundary$ $Layer$ mesh. We
show that the method converges uniformly, with respect to both singular perturbation parameters,
at an exponential rate when the error is measured in the energy norm. Numerical examples are
also presented, which illustrate our theoretical findings as well as compare the proposed method
with others found in the literature.</p>