Graded Galerkin methods for the high‐order convection‐diffusion problem | Zendy

Liu SongTao | Zendy; Xu Yuesheng | Zendy

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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

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