TY - JOUR
T1 - Local analysis of HDG methods for convection-dominated diffusion problems
AU - Jin, Yanyi
PY - 2016/3/22
Y1 - 2016/3/22
N2 - In this paper, we establish local error analysis of hybridizable discontinuous Galerkin (HDG) methods for convection-dominated diffusion equation in two types of subdomains away from the layers. The first subdomain is of O(log(1/h)h1/2) away from the interior layers and ofO(log(1/h)h) away from the boundary layers and the second one is of O(∈) away from the outflow of the boundary. Our local error bound for the first subdomain can be improved by a factor of log(1/h). We use weighted estimates to prove the first result by constructing new weight functions and the inf-sup condition of the bilinear form to prove the second one.
AB - In this paper, we establish local error analysis of hybridizable discontinuous Galerkin (HDG) methods for convection-dominated diffusion equation in two types of subdomains away from the layers. The first subdomain is of O(log(1/h)h1/2) away from the interior layers and ofO(log(1/h)h) away from the boundary layers and the second one is of O(∈) away from the outflow of the boundary. Our local error bound for the first subdomain can be improved by a factor of log(1/h). We use weighted estimates to prove the first result by constructing new weight functions and the inf-sup condition of the bilinear form to prove the second one.
KW - Convection-diffusion problems
KW - HDG method
KW - Local error estimate
UR - http://www.scopus.com/inward/record.url?scp=84963826916&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84963826916&origin=recordpage
U2 - 10.1016/j.cam.2016.03.014
DO - 10.1016/j.cam.2016.03.014
M3 - RGC 21 - Publication in refereed journal
SN - 0377-0427
VL - 304
SP - 57
EP - 72
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -