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Graded Galerkin methods for the high‐order convection‐diffusion problem
Author(s) -
Liu SongTao,
Xu Yuesheng
Publication year - 2009
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.20396
Subject(s) - mathematics , hermite polynomials , hermite spline , galerkin method , m spline , perfect spline , spline (mechanical) , convection–diffusion equation , mathematical analysis , singular perturbation , discontinuous galerkin method , partial differential equation , thin plate spline , finite element method , spline interpolation , physics , statistics , bilinear interpolation , thermodynamics
We develop a Galerkin method using the Hermite spline on an admissible graded mesh for solving the high‐order singular perturbation problem of the convection‐diffusion type. We identify a special function class to which the solution of the convection‐diffusion problem belongs and characterize the approximation order of the Hermite spline for such a function class. The approximation order is then used to establish the optimal order of uniform convergence for the Galerkin method. Numerical results are presented to confirm the theoretical estimate.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009