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

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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