TY - JOUR
T1 - A family of characteristic discontinuous galerkin methods for transient advection-diffusion equations and their optimal-order l2 error estimates
AU - Wang, Kaixin
AU - Wang, Hong
AU - Al-Lawatia, Mohamed
AU - Rui, Hongxing
PY - 2009/7
Y1 - 2009/7
N2 - We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG, and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangian methods and discontinuous Galerkin methods. An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context of advection-diffusion equations.
AB - We develop a family of characteristic discontinuous Galerkin methods for transient advection-diffusion equations, including the characteristic NIPG, OBB, IIPG, and SIPG schemes. The derived schemes possess combined advantages of Eulerian-Lagrangian methods and discontinuous Galerkin methods. An optimal-order error estimate in the L2 norm and a superconvergence estimate in a weighted energy norm are proved for the characteristic NIPG, IIPG, and SIPG scheme. Numerical experiments are presented to confirm the optimal-order spatial and temporal convergence rates of these schemes as proved in the theorems and to show that these schemes compare favorably to the standard NIPG, OBB, IIPG, and SIPG schemes in the context of advection-diffusion equations.
KW - Advection-diffusion equation
KW - Characteristic method
KW - Discontinuous galerkin method
KW - Numerical analysis
KW - Optimal-order L error estimate
KW - Superconvergence estimate
UR - http://www.scopus.com/inward/record.url?scp=67650951407&partnerID=8YFLogxK
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U2 - 10.4208/cicp.2009.v6.p203
DO - 10.4208/cicp.2009.v6.p203
M3 - Article
AN - SCOPUS:67650951407
SN - 1815-2406
VL - 6
SP - 203
EP - 230
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 1
ER -