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Convergence analysis of the LDG method applied to singularly perturbed problems
Author(s) -
Zhu Huiqing,
Zhang Zhimin
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21711
Subject(s) - mathematics , singular perturbation , piecewise , rate of convergence , norm (philosophy) , discontinuous galerkin method , bilinear form , exponential function , mathematical analysis , convergence (economics) , galerkin method , perturbation (astronomy) , finite element method , channel (broadcasting) , physics , electrical engineering , quantum mechanics , political science , law , engineering , economics , thermodynamics , economic growth
Considering a two‐dimensional singularly perturbed convection–diffusion problem with exponential boundary layers, we analyze the local discontinuous Galerkin (DG) method that uses piecewise bilinear polynomials on Shishkin mesh. A convergence rate O ( N ‐1 ln N ) in a DG‐norm is established under the regularity assumptions, while the total number of mesh points is O ( N 2 ). The rate of convergence is uniformly valid with respect to the singular perturbation parameter ε . Numerical experiments indicate that the theoretical error estimate is sharp. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013