TY - JOUR
T1 - Superconvergence of a Galerkin FEM for Higher-Order Elements in Convection-Diffusion Problems
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 356
EP - 373
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1320nm
UR - https://global-sci.org/intro/article_detail/nmtma/5879.html
KW - Singular perturbation, layer-adapted meshes, superconvergence, postprocessing
AB - <p style="text-align: justify;">In this paper we present a first supercloseness analysis for higher-order
Galerkin FEM applied to a singularly perturbed convection-diffusion problem. Using
a solution decomposition and a special representation of our finite element space,
we are able to prove a supercloseness property of $p + 1/4$ in the energy norm where
the polynomial order $p ≥ 3$ is odd.</p>