TY - JOUR
T1 - A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems
AU - Tabata, Masahisa
AU - Uchiumi, Shinya
PY - 2016/2/1
Y1 - 2016/2/1
N2 - We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.
AB - We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.
KW - Convection-diffusion problems
KW - Exact integration
KW - Finite element method
KW - Lagrange–Galerkin scheme
UR - http://www.scopus.com/inward/record.url?scp=84958035944&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84958035944&partnerID=8YFLogxK
U2 - 10.1007/s13160-015-0196-2
DO - 10.1007/s13160-015-0196-2
M3 - Article
AN - SCOPUS:84958035944
SN - 0916-7005
VL - 33
SP - 121
EP - 143
JO - Japan Journal of Industrial and Applied Mathematics
JF - Japan Journal of Industrial and Applied Mathematics
IS - 1
ER -